Research on evolving design and evaluation of the HIPLEX program: final technical report

Report 82-7
RfSE;';:'f'J! ON EVOLVI~ resIGN AND EVAWATION OF
mE HIPLE:X PROGRAJ>l: FIP\AL !EOOICAL REPORT
By: P. L. :::aith, P. w. lo!if!lke, Jr•• • K. J. Berry:
A. A. foneaud, R. D. Farley, J. H. Hirsch,
P. J. J."opp, J. R. Miller, Jr •• H. D. Orville.
and D. L. Priegnit%
Rovember 1982
Prepared for:
Division of Atmospheric Resources Research
Bureau of Reclamation
U.S. Oepartment of the Interior
Box 25007, Denver Federal Center Contract No. 8~07-83~V0009
Denver, CO 80225 dated 15 December 1977
Institute of Atmospheric SCiences
South Dakota School of Mines and Technology
Rapid City, South Dakota 57701
·Colorado State University. Fort Collins. CO 80523.
=::~-:~-"l""
,. REPORT NO.
Insti tute of A.tlJOspheric Sciences
S.D. School of Mines and Technology
Rapid City, SD 57701
·D\"v°iN:~~ri."oAr~f.rix,N;p'Yic"r"fc ~eRs~~rces Research
Bureau of Reclamation
U.S. Deparwent of the Interior
Box 2500~;" D:~~~~ Federal Center
8-07-83-VOOO9
Final Report
Dec 1977 - Nov 1982
Subcontractor _ Colorado State University. Fort Collins, CO 80523
This report summarhes five years of research related to the design,
conduct, and evaluation of the U.S. Bureau of Recllllllation's HIPLEX progran
Most of this research concerned the IIlPLEX-I experilllent that involved
randomhed seeding of small "lontana cUliulus congestus clouds with 'dry ice.
The report discusses the design, conduct, and response variables of
UIPLEX-I and presents a statistical evaluation of the experiaent. Ie also
surlllllarizes the results of related physical, statistical, and nUll:erical
cloud JIOdeling studies. The physical studies included analyses of HIPLEX
aircraft, mesonet, radar, and rain gage data. The sutistical investi­gations
were concerned uinly with the deve10JDent and application of the
wIti-response pertlUt;ation procedures (MRPP) used for the statistical
evaluation of HIPLEX-l. The numerical r=odeling studies included
silllUlations of each of the HIPLEX-I test cases.
'7. N~V WORoS ANO OO<::UN£IIT ANALVS'S
DESCRIPTORS-- wcather modification, cloud modification, cloud physics,
cloud seeding, precipitation (atmospheric). rainfall, cloud IIlOdcls,
meteorological radar, statistical Illetho<ls, convection clouds, cumulus
clouds, clllllUlonimbus clouds, atmospheric research (A.uthority:
"Thesaurus of Water Resources Terms"); mesoscale analysis
b. IOENTIFIERS.. .
High Plains Cooperative Progr8ll (IIIPLEX)/Project Skywater
cos...n Fi.,I11/Group COl\'RR 0402.1
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TABLE OF CONTENTS
ABSTRACT ..•••••
LIST OF FIGURES •••
iii
LIST OF TABLES • • • • •
1. I/IITRODUCTION .••
2. BACKGROUND: OVERVIElI' OF llIE HIPLEX PROGR,AN ••
3. THE DESIGN AND CONDUCT Or HIPLEX-I ••••••
3.1 The Randomhation Procedure ••.••••
3.2 Boxing of the Radar Echoes for Test Case Clouds •
3.3 Values for the HIPLEX-l Response Variables ••
3.4 Checks of Values for the HIPLEX-l Response
Variables •••
3.4.1 Radar. • • •
3.4.2 Aircraft •••••••••••••••
vi
4. STATISTICAL STUDIES •••••••••••••••••
4.1 Development of ~tulti-Response PeI'1llUtation
Procedures (MRPP) • • • • • • • . • • • • • • 9
4.2 Prelillinary Sample Site Estiaates for HIPLEX-l • 10
4.3 Statist.ical Evaluation of lUPLEX-l • • • • • • • • 14
4.4 Final Test. Statistics for HIPLEX-l • • • . . • • • IS
4.5 Results of a Classical Rank Test Applied
to HIPLEX-l Test Cases • • • • • • • • • • 18
4.6 Representat.ive Draw Analysis. • . • • • • • • 20
4.7 Estimated MRPP P~Value Dependence on Suple
Size for HIPLEX-l • • • • • • • • • • • 20
5. PHYSICAL INVESTIGATIONS • • • • • • • • • • • • • • 24
5.1 Raindrop Site Distribut.ions and Z-R
Relationships in HIPLEX-l • • • • • • • • • • • 24
5.1.1 Characteristics of the data. • • • • • • • 24
5.1.2 Drop size distributions. • • • • • • • • • 25
5.1.3 Z-R relationships. • • • • • 27
5.1.4 Comparisons between aircraft
and radar data • • • • • • • • • • • • • 30
iv
TABLE OF ~Ta"S (continued)
5.2 Studies of Non·Test-Case Clouds ••••••••• 31
5.3 Mesoscale Analysis. • • • • • • • . • • • • • • • 3A.
5.4 Est~ates of Requirements for I-leasuring Rainfall
fTOIl Convecdve Complexes with Rain Gages. 35
5.4.1 SUlJUry of results •••••••••• 36
5.4.2 Principal conclusions. • • • • • • ~8
5.5 Comparison of Gage and Radar Measurements
of Rainfall from Convective COlllplexes • 39
5.5.1 Data acquisition and reduction • 40
5.5.2 Summary of results •••••••••••• 41
6. NUMERICAL CWUO MODELING STUDIES •• • • • • • • • • • 45
6.1 Addition of a Snow Field to the Model •••••• 46
6.2 Addition of Convergence Effects to the Model. • • 46
6.3 TiDle-Step Effects in the Model Rcsul ts • • • • • • 47
6.4 Simulation of Silver Iodide Seeding in the Model. 48
6.5 Dyn8Jl!ic and ~licrophysica1 Effects
of Silver Iodide Seeding . • • • • • • • • • • 48
6.6 Simulation of Dry Ice Seeding in the Model. 51
6.7 Sim.dation of IIIPLEX-l Test cases • • • • • 52
6.8 Co..parison of Model Outputs with Actual
HIPLEX-l Observations • • • • . • • • • • 54
6.9 SillUlation of Convective Precipitation
with the 1oIode1 60
7. SlMlARY M1) CQ;"CWSION • • 62
ACKM:».'L.EJ)(}(ENTS ••••••••
REFERENCES • • • • • • • • • • •
APPENDIX A: Coordination Meetings During Period
1 April 1981-30 Novelllber 1982 •••
APPENDIX B: mpl.EX-l: Experimental Design and
Response Variables ••.•••••
APPENDIX C: HIPLEX-I: Statistical Evaluation ••
APPENDIX D: List of Publications Prepared Under
This Contract ••••••••
APPENDIX E: List of Project Personnel •.•••.
63
70
71
103
l20
126
LIST OF FIGURES
Humber Title f!&!.
Four cUllI.llative drop she distributions from
HIPLEX-I Case No.9 (22 July 1979). with
overlapping sample volurucs 2.
Z-R scatter diagram for the composite drop
size data from all the HIPLEX-l test cases
froa 1979 and 1980 • 2.
Histograas showing the percent of seeded and
non-seeded 1978 clouds having various values
of average u.'C at 0, S, 8, and 10 lIin after
"treatment" tiJne • 32
Plot of average and standard deviation of
Johnson-Williams LWC for 1978 seeded and
non-seeded Class A clouds vs. tiJlle. 33
Median of the absolute values of the relative
errors in gage estimates of rainfall volwnes
as a function of the nlunber of gages
receiving rain from a complex 37
Scatter diagra. cOll1paring radar estimates
of rainfall volurues for convective
complexes with rainSlo'ath areas . 3.
COlllparison of frequency distributions of
IS-Illin rainfall events £rolll 21 June 1977
as observed by two different methods 41
Normal probability plot of the log ratios,
log(GER/RER), froll 21 June 1977 data • 42
Example of tillle plot of IS-Din rain amounts
for one gage location (GER' and RfR events) • 44
10 The accumulated rainfall vs. tillle since
model initialization in the seed and
non-seed versions 52
11 NlJIlericRI siJwlation at 72 lIin .cdel time of
HIPLEX-l Test Case No. 10, 23 July 1979
(Class A-I cloud) 54
vi
LISI' OF FIGURES (continued)
12 Profiles of state variables and wind cOlllpOnents
across cloud model domain at height 4.4 kID,
after 12 min of simulated time. • • • • • • • • Ss
13 Simulated aircraft sample of clouds taken 3.8 km
above ground at 57 min of model time, or about
S min after treatment tilQe • • • • • . • • • • • • 57
LIST OF TABLES
Estimated power (I-II) of HIPLEX~l MRPP tests
for high, low (actual), and conservative
seeding effects • • • • • • • • • • • • • • • 13
Point estimates and MRPP test results for the
final test statistics • • • • • . • • • • . 17
Univariate Tank test results ~ HIPLEX-l • • • • • 19
~eans and standard deviations of "representative
draw" variables • • • • • • • • • • • . . • • 21
Changes in MRPP univariate P-values for raw
data values if observed data sets weTe
doubled and tripled. • • • • • • • • • • • • • 22
Comparison of lIOdel generated and observed
cloud response variables - HIP23 • • • • • 43
COlllparisons for all cases producing clouds
in model ••• • • • • • . • • • • • • • • 58
Comparisons of precipitation estimates for
cases producing clouds in model • • • • • • 61
1. Itm!ODUCTION
This is the final technical report submitted by the South Dakota
School of Mines and Technology (School of Mines) on research carried
out under the subject contract. Under this contract. personnel of the
School's Institute of Atmospheric Sciences (lAS) assisted the Bureau of
Recllllllation (Bureau) of the U.S. Department of the Interior in the
design and evaluation of the HIPLEX pFlgralll. The work was carried out
in collaboration with personnel of Colorado State University (CSU).
who were responsible for carrying out DOst of the statistical work
required to fulfill the project objectives. Work under the contract
extended over a pe1'iod of five years. beginning in DecCMber of 1977.
A series of interim progress reports (Dennis et aI •• 1979. 1980;
Smith et al •• 1981) describe the basic adDinistrat'iVearrangements for
conductrnithe work. The CSU participation "'as carried out under a
subcontract negotiated with the School of ~lines. The interim reports
sumnarited progress on the research being carried out und<lr the con­trC\
cts. Many of the resul ts of that research have appeared, or are
pending. in the f0rDl31 scientific literature or in conference pro­ceedings
and similar documents. 1he HIPLEX progralll also involved
many other participants from federal. state. university, and private
organizations; reports of their work will appear in a variet.y of for­mats.
Consequently. the present report attellpts mainly to highlight
the significant results of the research carried out under the subject
contract. No consistent attempt is made to present the colllplete details.
to give a complete chronology of the way the results were attained. or
to place them properly within the context of the overall HIPLEX
program.
The administrative procedures followed and related matters will.
for the llIost part. not be treated in this report. One aspect. however.
deserves lIlention because of its importance to the success of the
overall research effort. That is the series of coordination meetings
held between School of Mines and esu personnel. Those meetines. held
to coordinate the scientific effort and plan future activities under
the contract, played an mportant part in the overall conduct of the
project. About 10 such meetings were held each year. until the curtail­ment
of contract funding caused the frequency to be reduced during the
last year and a half of the period.· Representatives of the Bureau and
other HIPT.EX participants frequently participated in the meetings.
depending upon the location. schedule. ano subject matter on the agenda.
Appendix A tabulates the coordination meetings held since the date of
the last interim progress report (April 1981).
2. BACKGROUND: OVERVIEW OF llIE HIPLEX PROGRAM
The High Plains Cooperative Progrlllll (HIPLEX) is a joint federal/state
effort to develop practical .eans of stiJllUIating rainfall over the
High Plains region of the Uni ted States. The Division of At:l:lospheric
Resources Research of the Bureau of Re<:l&lftation in the Department of
the Interior is the federal agency responsible for the overall direc-tion
of HIPL£X. Field work, related U1eoretical and laboratory studies,
and data analysis have been carried out by 8 Il1..IEber of federal and state
goverTllllcnt agencies, as well as university groups and private fil'llls.
Activity under the HIPLEX program was carried out at field sites near
"liles City, f.tlntana; Goodland, Kansas; and Big Spring, Texas; beginning
as early as 1974. 'l1\e last field work directly associat~d "''ith HIPLEX
was conducted at Miles City in the summer of 1980, althol.lgh HIPLEX
groups participated in the Cooperative Convective Precipitation
Experiment (eCOPE) at the same site in the summer of 1981.
The major activity under the present contract was related to the
HIPLEX-I experiment conducted at Miles City. Substantial contributions
were made to the design of that experiment, which is spelled O\lt in a
design document (Interior, 1979). It involved randomized seeding of
SIlIall cumulus congestus clouds with dry ice in an effort to accelerate
the fOTlllation of precipitation. Wor};. under the contract included
monitoring the progress of the experislent in the field and continuing
review and updating of the experiment design as necessary. ThM
required assessing the impact of various design options on the
planned evaluation of the experiJ:lent and assisting Bureau personnel
in selecting the .ost suitable options. Following the termination of
HIPLf.X-I after the 1980 field season, due to the a<hrinistrative "llOth­balling"
of the program, a statistical evaluation of the experiJaent
"'"as conducted. SillK1lations of the seeding experiments toere also carried
out using a n.u:!eric.e.l cloud .ode!, and a variety of physical evalua­tions
of HIPLEXwl "-ere performed. A follow-on experia:ellt on larger
cloud systeJ:IS, called convective colLplexes, vas contelllplated as a
further part of the HIPLEX program, and planning studies related to
the design of such an experiment were carried out. However, at this
juncture it is not <:lear whether such an exreriment will ever be
conducted.
The design of the HIPLEX-l exPe~iJlent (Interior, 1979) included a
detailed physical hypothesis regarding the effects of seeding with dry
ice on the development of precipitation in selected small cumulus con­gestus
<:louds. The process of cloud selection involved a set of prelim­inary
aircraft and radar measurements to determine whether conditions
corresponding to those assumed in the experimental design actually
existed in the subject <:louds. Suitable clouds were classified into
three categories (called A-I, A-2, and B) on the basis of criteria
intended to detemine the likelihood that precipitation would develop
naturally in the clouds. TTeatment was carried out using a double blind
type of randomization to determine which of the selected clouds were
to be seeded with dry ice dropped from a jet aircraft. Thirteen pri­mary
and eight secondary response variables vere measured by aircraft
and radar to check the various steps in the physical hypothesis. The
statistical evaluation of the experiment was based mainly on ''IIIulti­response
penutation procedures" (MRPP), lihich -.rere devol oped by the
CSU particpants ur.der this can'tlact. .:>eparate physical evaluations
of the measuresents are being conducted by various HIPLEX participants
to confirm the physical ur.derstanding of effects of seeding. As men­tioned
above, numerical simulations of the seeding experiments have
also been carried out to simulate the behavior of the tost case clouds
and their responses to the seeding treatrr.ents.
The research carried out under this contract can be divided into
four broad general categories:
The design and conduct of the HIPLEX-I experiaent,
including calculation of the response variables.
b. Statistical studies, including the statistical
evaluation of HIPLEX-l.
Physical analyses, related directly or indirectly to
HIPLEX-I or to contemplated follow-on experiments.
d. NUlI!erical cloud modeling studies, including sillulation
of the HIPLEX-I test cases.
In the following sections, brief SUJm'.aries of the research under each
of these four broad areas are presented.
3. TIlE DESIGN AND CONDUCT OF HIPLEX-l
A major portion of the effort under this contract was devoted to
assisting with the development of the experimental design for HIPLEX-l
and monitoring the conduct of the experiment. Work under the contract
included preparation of two of the appendices to the design document
(Interior, 1979):
Appendix B: Conceptual Models ano Physical Hypothesis,
by A. S. Dennis and Ii. D. Orville
b. Appendix E: Statistical Design and Evaluation, by
P. W. Mielke, Jr., ar.d A. S. Dennis
A manuscript discussing the design, conduct, and response variables of
the experiment is included as Appendix B to this report: it has been
submitted for consideration for journal publication. The manuscript
gives an overview of the experimental design and the conduct of the
experiment; provides a synopsis of the procedures used to calculate the
response variables; and tabulates their values for the 20 HIPLEX-l test
cases from 1979 and 1980.
Substantial contributions were made under this contract in the
following specific areas:
1. Establishment of the randomization procedure for allocating
treatments to experimental units.
2. The. formulation of the physical hypothesis.
3. Statement of the statistical hypotheses for the experiment.
4. Definitions of the response variables, including default
values, and the procedures used in collecting the data
and calculating values for the response variables.
S. Establishment of the multi-response peTlllUtation procedures
(~lRPP) used in conducting the statistical evaluation of
the experiment.
6. A partial simulation of the experiment, using data from
exploratory field studies carried out in 1977 and 1978,
to estimate the required sample size for the experiment.
7. Monitoring the conduct of the experiment in the field.
8. Calculating the radar-related response variables and
checking the calculations of the response variables made
by other IIIPLEX-l pllrticipants.
9. Issuing the "official" tabulation of the response variables.
The status of most of these aspects of HIPLEX-I is sullllllarited
adequately in Appendix B. Some additional colMlents on three of the
areas appear in the follo....ing subsections, and other sections of this
report deal with topics related to some of the other areas above.
3.1 The Randomiution Procedure
Section 4 of Appendix B outlines the double-blind type rando.hation
procedure et!lployed in HIPLEX-l. It nquired the preparation of one set
of "dispenser disable" randollli~ation envelopes, based on an unrestricted
randomization, to deteX'lline "tlich of the two dry ice dispensers on the
seeding aircraft was to be disabled for a given flight. One of those
envelopes was used before each flight, including flights on which no
suitable test case clouds were found.
Six additional sets of "dispenser selection" envelopes 101ere prepared
for use in detel'llining which dispenser should be activated by the crew
of the seeding aircraft once a candidate cloud had passed the selection
criteria for a particular class. Two sets of these envelopes ,,-ere needed
for each cloud class (A-I, A-2, or B), with the one used for a particular
flight being chosen according to which "dispenser disable" decision had
occurred. In that way, the restricted non_seed/seed randomization for
test cases wi thin each cloud class was preserved regardless of the disable
de<:ision or the class of cloud encountered on a given flight. Two
envelopes from the appropriate set for each cloud class were taken to
the HIPLEX radar site as each flight was being launched, because a
maxillUm of two test cases could be treated on anyone flight. Therefore.
three pairs of envelopes were on hand at the radar site during a flight,
and an envelope appropriate to the particular cloud class was opened
after a test case cloud had been selected. Any unused envelopes t;ere
returnee. to the appropriate stack after each flight.
Further details of this procedure are contained in memoranda that
arc being stored with the HIPLEX-I archives at the Division of AtJnospheric
Resources Research Office in Denver, Colorado. ThE' decision card in each
envelope was signed and dated by the person who executed the appropriate
instructions, and the used envelopes and cards are also in the archives.
Proper execution of the procedure vas verified against the oriainal
rando.ization sequences by a statistician, and the verification log is
in the archives as 101e11.
3.2 Boxing of the Radar Echoes for Test case Clouds
Before the HIPLEX-I rlldar response variables could be computed so
that statistical and physical analyses could be perfomed, the radar
data had to be examined to dctemine which echoes came froJll the test
case clouds. The process of separating or identifying the relevant
echoes, called ''boxing,'' involved detemnifli range and a~illluth
boundaries around the echoes on printouts of data froll slant PPJ
displays. To guard against any unintentional bias llhen boxing the
eehoes, it was ilI,portant that the analyst be isolated fTo_ the aetual
operations period and be unaware of the treatllent decisions. Therefore
she ",as not allowed to visit the Miles City field site during the aetual
HIPLEX-I field operations, and she was not infonted of the treatment
decisions until aftor the boxing proeess had been colllpleted. Moreover,
she was furnished ldth an excess of radar and other data nth coded dates,
so that she did not even kno.... whieh data corresponded to actual HIPLEX-I
test cases.
Data in addition to the radar data were necessary to determine
which echoes came from the test case clouds. The data included plots
and listings of the FAA flight tracks for the HIPLEX-I aircraft (King
Air, Learjet, and Twin Otter); printouts of colllpOsite and single-scan
PPI radar displays at a scale of 1:250,000; edited transcript.s of air­craft
and radar crew voice notes (all recorded prior to the first post­treatment
pass); till-e-height plots for the Learjet; and King Air initial
pass lengths amI pointer positions.
Although a certain amount of subjectivity was inherent in the
boxing process, gUidelines were established and followed ....'hen boxing
the HIPLEX-l echoes. The steps taken included the following:
1. Transfer the aircraft flight tracks, cloud pass lengths,
and pointer positions to the composite radar printout.
2. Calculate a diffusion circle radius, r, for each radar
volUlle sean using the equation
r .. 2 X 10-5 ../3OO"""tT
where r is in 1an and t is the tille after treatment in
seconds. For t < 670 s (11.16 .in), a radius of 6 };m
....as used; for t > 1494 s (24.9 _in), a radius of
20 km was used.
3. Determine which echoes were due to aircraft "skin paint"
reflections. This was done by a) coWlparing the time and
loeation of the echo with the positions of the aircraft
at that ti~\e; b) comparing .the echo height with the alti­tudes
of the aircraft at that time; and c) judging ....nether
the echo was continuous in time or only occurred on one
scan. The possibility of an echo being due to skin paint
was not considered if echoes ",ere recorrled in several
radllJ" data bins grouped together in an area, or if the
echo was recorded at several elevation angles.
<\. Study the transcribed voice recordings to detennine "!<oilat
types of clouds were in the areo and ....nether the test
case had any neighboring turrets.
(1)
,
5. EXIllline the flight tracks and the radar data to pick out
the echoes which most likely 1o'ere froll the test case.
following the same echoes through til:le.
6. Box the echoes selected on each voIUlIIe scan in teI'lls of
intervals of range and azimuth that could be used to
delineate the echoes for computer processing of the data.
Since certain judgments had to be made in many iflstances, a written
record was kept of the rationale used in determlning the test caso
echoes.
Along with the 20 HIPLEX~l test cases, echoes £rolll 76 additional
eases were boxed (57 from 1979 and 19 frolll 1980). 11v:lse extra cases
were froe clouds that were studied prior to the official beginning of
the experiment. when both aircraft were not available. or ,men they
did not lIleet all of the selection criteria as HIPLEX-l cloulb. They
were included to make it ItOre difficult for the analyst to detemine
anything about the actual test cases, as well as to increase the
overall data base for p~ysical analyses.
The coordinates of the boxes defined for the 20 HIPLEX-l test
cases are listed in earlier reports (Dennis et al., 1980; smith et aI.,
19B1). These boxes \o:ere cOlllpared to ones de'HnecrbY an independent­analyst
in Miles City, who I\'as present during the field operations and
therefore had some knoWledge of the treatment decisions. The definitions
were found to be in good agreement, suggesting a reasonable aJIlo\mt of
objectivity in the boxing process.
3.3 Values for the HIPLEX-l Response Variables
Computed vtllues for the HIPLEX-l primary and secondary response
variables are presented in Tables 5 and 6 of Appendix B. Values for
the final test statistics appear in Table 5 of Appendix C. Consider­able
effort in HIPLEX-l was devoted to cross-checking the procedures
used and the resulting values of the response variables. That aspect
of the work under this contract is discussed in Sec. 3.4.
Rank-order listings of the response variables for the Class A-I,
Class B, and pooled Class A-I and B clouds were also prepared for use
in the statistical evaluation of HIPLEX-1. The rank tables are too
lengthy to reproduce here, but are available in a Me!r.orandUID for the
Record by James R. Miller, Jr., dated 30 July 1982. [Of course they
can also be reconstructed from the tables of values for the response
variables themselves.]
3.4 Checks of Values for the HIPLEX-I Response Variables
To insure that accurate values "'ere obtained for the response
variables, a variety of manual checks Yere perfomed under this con­tract
as veIl as by other HIPLEX participants. Although some....hat
tedious and time consuming, these checks proved valuable in locating
problems in obtaining the proper computer generated values. Tlro dif­ferent
data sources (radar and aircraft) were used to generat.e the
response variables, SO two different types of checks were e"ployed.
3.4.1 Radar
The radar response variables, both priJ!lary (TFE. TIPR, RERC) and
secondary (M2EA, M3EA. D2EC. D3EC, TIF3), were determined manually for
selected test cases fY'Olll dumps of the radar "dBz file" data. Each
duJllP consisted of a COWlputer printout of Z values for indiviC,ial
radar data bins at the various antenna tilt angles and tiMes. Those
bins falling within the echo box boundaries "''ere flagged and the data
tabulated separately. FrOIIl these, echo intensities, areas, volumes,
etc., ,,-ere dete:m.ined from which the applicable response variables
were calculated. Several discrepancies "'ere found between the com­puter-
generated and manually generated values. These discrepancies
(such as an erroneous TFE in one case) were quickly corrected. 1bis
process clearly illustrated the need for dotailed checks of this sort.
3.4.2 Aircraft
The primary reduction and initial analysis of the aircraft data
were carried out by University of Wyoming personnel. Independent
computer-generated values were obtained by Bureau of Reclamation per­sonnel
at Miles City to the extent practical. so that the independent
computations could be cross-checked. School of Mines personnel lIIade a
few mlmlal spot checks of sOll:e of the collluter-generat.ed values. These
checks ,,-ere intended to verify the computer-generated response variables.
Colllparisons led to discussion and subsequent recalculation of Dny
variables where minor discrepancies or errors were identified.
The process of having several research groups independently uke
these checks helped insure the accuracy of the resul ting response vari­ables.
On the surface it may reflect SOlie redundancy, oot in this
experiment the checks proved very valuable. School of Nines personnel
'WOUld re~end that plans for future weather modificat.ion projects
allow for independent checks of the data gathered and tabulated for
subsequent analysis.
4. STATISTICAL STUDIES
A variety of statistical investigations were carried out under
this contract. Most of this work was related to the development and
application of the wlti-response permutation procedures (MRPP) that
were used as the primary ~thod for the statistical evaluation of
HIPLEX-1. The following subsections sllt'lllarize that work plus other
related statistical studies.
4.1 Development of ~\J.lti-Response PeT'lJlUtation P'rocedures (MRPP)
Prior to the beginning of the present project, only tlo"O preliminary
articles inVOlving an inefficient version of multi-response permutation
procedures (MRPP) had been either published or subnittcd for publication
(Mielke et al., 1976; Mielke, 1978). Those t\lfO articles provided effi­cient
computation procedures and also deD:lnstrated that the distribution
of the f.IRPP test statistic at tilles departed substantially from nomality
for both finite and infinite sample sizes.
The initial paper under this contract ()lielke, 1979a) introduced
a univariate rank test based on MRPP "tdch depended on Euclidean dis­tance,
a point that was later recognized to be of major importance.
The next project paper on ~lRPP (Mielke, 1979b) introduced the presently
used efficient version of ~PP. O'Reilly and ~~ielke (1980) charac­terized
conditions when the as)'ltptotic distribution of t-lRPP statistics
is normal and also introduced the presently used general version of
the MRPP statistic. Brockwell et a1. (1982) described the aSYlDptotic
distribution of the MRPP statistic""1Or the univariate case lrihen
asymptotic nomality fails.
Mielke et a1. (198la) intuitively motivated the use of ~m.PP with
Euclidean distance as the distance function (without fully apprecitlting
the reason fOr this motivation) and also introduced the Pearson Type
III distribution approximation for the P-value (previously a lIIOre
complicated beta distribution approxilllation for the P-value had been
used). MieUe et a1. (198Ib) provided Monte Carlo power COIllparisons
which suggested"8"dvanuies for rank tests based on a distance function
involving Euclidean distance over classical rank tests based on a dis­tance
function involving squared EuJ:l.idean distance (the latter being
the Wilcoxon-Mann-lOlitney test). A procedure for obtaining exact f.IRPP
P-values was developed by Berry (1982) for cases (like HIPLEX-l) when
sample sizes are relatively small. ~!ielke and Berry (1982) and melke
and Iyer (1982) provided variations of MRPP which handle matched pairs
and randomized blocks, respectively. While Mielke et a1. (198lb)
initially pointed out the geometry problem associatea WIth classical
penlutation tests in a subtle _nner, Mielke et a1. (1982) elIlphashed
the fact that only the choice of Euclidean distance as the distance
function yields perlmtation tests with an analysis space which is
10
compatible with the data space. (Many classical permutation tests,
such as the Wilcoxon-Mann-Whitney test and the peI'll!Utation version of
AN)VA. were shoft'll to have an analysis space ....'hich is not compatible
with the corresponding data space.) The I>lRPP large sample program
has been documented by Bert')' and Mielke (1983).
All of the above-cited papers (except the two preliminary papers)
were project papers which proVided substantial contributions to the
development of "IRPP. As a consequence of the effort summariz.ed above,
requests have been received from the editors of both the Handbook of
Statistics, Vol. 4, and the Encyclopedia 2! Statistics, ~o­prOVIde
sUl':IflIsry papers of MRPP.
A few additional papers not directly related to MRPP ",~re also
prepared during this contract. These illcluded a paper pertaining to a
theoretical distribution problem inherent in certain classical linear
rank test statistics (Mielke and Sen, 1981) and a paper on the Climax I
and II experiments (Mielke at ~ 198Ic). Furthel'll\ore, a chapter was
prepared for a book on statIStlcs in atmospheric science (?>lielke, 1982).
4.2 Preliminary Sample Size Estimates for HIPLEX-l
This section describes the procedure used for estimating the
sample sizes needed to detect specified seeding-induced changes in
IlIPLEX-l. This procedure was employed prior to the beginning of
HIPLEX-I and the resul ts were used to estimate the required length
of the experiment (see AppendiX E of Interior, 1979). Given specj­fied
values of the type I and type II error probabilities (a and S),
the sample size estimates were based on the Euclidean distance
version of the mul ti-response permutation procedures (MRPP).
In comparison to 1\-ell known power calculations for parametric
tests which assume an underlying normal distribution (or perhaps some
other well defined distribution), analogous calculations for pemutation
tests are exceedingly more difficult. In addition to the dependence
on (1) the level of significance; (2) the sample-size structure; and
(3) the fonn of the alternative hypothesiZe<! for a seeding treatment,
power calculations for permutation tests also depend on (4) the type
of distribution in question. As a consequence, the only feasible way
to obtain the power characteristics. Qf permutation tests is through
simulation. While simulation is admittedly slow and cumbersome, the
resul ts of such an effort will likely be far lOOre realistic than
results based strictly on convenient artificial premises. The pro­cedure
for obtaininR the power characteristics associated with ~lRPP
follo,""s.
Because tho power chnrflcteristics of permutation tests (lrc highly
dependent on both the actual distribut.ion and the hypothesized alter­native
in question, it is important that reasonable approximations be
11
obtainable for both of these quantities. As a consequence. a five-~ari
simulation ~am was construeted which will yield power~charaetenst c
:e:~:\;~: 0/un~:~~S c::e~iC~~~O~ ~eth~:t~~~b~:qUires
description of the data in question (previous observations usually
provide the best source of this inforsation). A .ember of the data
base may consist of either just a response variate or a pair consisting
of both a response variate and a predictor. A data base of paired
values is needed for a simllation ir.vc1ving residuals. With the data
base available in a listed foI'WI. a large number of randoll samples
(e.g •• SO) of a specified she (e.g., 50) are then selected (with
or without replacement being an option) from the data base.
vaTia~: SsffihO;r~~o:~~:a~:)b~n:~~~~g~:;r~~i:~~e::~u~::~:~
and (b) performs selected scale and/or location adjustments to the ran­dom
portion of the response variates designated as seeded. Let an ith
response measurement and corresponding predictor for a seeded case be
respectively represented by x.. and p.. (i" I ••.. , rand j = 1,
•.•• n!). Similarly. let an HK respofi~~ measurement and corresponding
~~~~~.~r (io~ ~. n~~~:e;d:~dcr
s
: t ~~~~ect~:el~e:~~e::t~~n~~e~U~
residulrs of the ith dimension aTe respe~ively denoted by
..'"
~e~ebi~c;:i~ a;~:::a i~~na~~~~:~~hf~~s;:;~s; ~:;::;~~: :A~ c·S
is the scale adjustment for a seeded ith response .easurement. If the 1
predictor corresponding to the ith response measurClJlent is not included.
:~~"tM~ :IR~~~N .. O. This part of the si.JmJlation program provides the
The third ~ of the program yields the MRPP test statistic (6).
the first""""three moments of 6. and t"hii skewness of 6 (Y6)' Most of the
computations of this simulation program are accomplished in this part.
~et~e~n~~:~::a~i~~v~~~~r~~~~o~s f~~j~:~~dr:~~i~~~ :~~;n:~:-
tistic (Le •• the P-value of each TB is based on the beta or Pearson
Type III distribution with the computed parameters c and d). The fifth
~ orders the obtained P-values (say, SO P-values for the puTposeoT
TITUstration) from smallest to largest. If the level of significance
«(I) is set equal to 0.10. then the estimated power (1-B) is merely
the proportion of the SO P-values ";hich are less than 0.10. Thus the
flOwer ca.n be easily estilllllted for any specified level of significance.
12
Because the power is a function of the sample size, this sU1ulation
progr3ll must be repeated for a IU:lber of different sample sizes (say, SO,
100, 150, and 200 cases, were half the cases are seeded and half are
non-seeded) in order to estil!ate the duration (s8IIple size) required of
this e~erilllcnt for specified eITOr probabilities (e.g., a" B· 0.10).
This shulation program rost also be repeated for each distinct choice
of the alternative hypothesized for a seeding treataent.
A small set of .e:uurements of six of the HIPLEX-I response variates
(CIC2. CIC5, PIC8. AlI"ca. TfPI, and 'I'FE) was collected as part of the
randol!lized calibration seeding trials carried out 'luring the initial
exploratory studies under HIPLEX. Two seeding ntes ld.th dry ice "''ere
employed in these trials: l.0 lc:gj1ar:, denoted as the high rate, and
0.1 kf/m denoted as the low rate. The low rate was adopted as the
actual seeding rate for HIPLEX-l. Those measuretllents provided the data
base needed for the first part of the simulation program, as well as a
basis for estimating the location and scale adjustments applied in the
second part.
A simulation of the proposed HIPLEX-l experiment was then carried
out using three of the response variables (CICS, PIC8, and TFPI).
Based on a level of significance (a) of 0.1, the estimated power (I-II)
is presented in Table 1 for various sample sizes (N) ...nen half the
cases arc assultcd seeded and the ranaining cases are asslllllcd
non-seeded.
For the high seeding rate effects, the results of Table 1 indicate
that a total sUIPle of 50 cases (25 seeded and 2S mn-seeded) would be
IIOre than adequate for Slltisf)i.ng the specified error probabilities
(a '" II = 0.10) with the three response variates considered individually
or jointly. In addition. a total sUlple of SO eases (25 seeded and 25
non-seeded) would also achieve the sase specified error J,robabilities
for TFPI and the three response variates analyzed jointl)" with the low
(actual) seeding rate effects. A total satlPle of 100 cases (SO seeded
and 50 non-seeded) would be llIOre than adequate to satisfr these same
specified error probabilities for the low (actual) seeding rate effects
when CICS and PICS are considered individually. "''hen the hypothesized
conservative seeding effect is considered, a total sample of 100 cases
would be adequate to satisfy these error probabili t.ies only for TFPl.
A total sample size of 150 cases (7.5 ,seeded and 75 non-seeded) is
adequate to satisfy these error probabilities Irrr'"ith the hypothesized
conservative seeding effect for PICS and the three response variates
analyzed jointly. unfortunately, even a total sample of 200 cases
(100 seeded and 100 non-seeded) is not adequate to satisfy these error
probabilities for CleS with the hyp"Otnesized conservative seeding effect.
Because the low seeding rate was actually chosen for HIPLEX-l.
the sample sizes estimated on the basis of effects measured tiith this
rate were considered to be the most realistic. The low seeding rate
13
ABLE I: Estmated power (I-~) of HJPLEX-I MRPP tests for high, low
actua ,and conservative seeding effects, when the level of significance
(a) is 0.1 and the total sample size (N) is as specified (N/2 cases are
eeded and N/2 cases are non-seeded). The response variate designated
OINT indicates that the three separate response variates (eICS, PICS,
nd TFPI) were treated jointly as a multi_response variate (specific
___~~~~~:~~~ _~~ ~~~:~~:~_~~~ _~! t'_=_~: _~~~_=_::~~_ ~~_ ~~~_:_~~~: _
Sample Response Seeding Effect
Size N Variate Hlgh Low Conservat.i'lie
SO CICS >0.99 0.66 0.10
PIC8 >0.99 0.82 0.20
TIPI >0.99 >0.99 0.70
JOINT >0.99 >0.99 0.40
100 CICS »0.99 0.95 0.10
PIC8 »0.99 >0.97 0.60
TFPI »0.99 »0.99 >0.95
JOINT »0.99 »0.99 0.60
ISO CtCS »0.99 »0.95 0.20
PICa »0.99 »0.97 >0.95
TFPt »0.99 »0.99 »0.95
JOINT »0.99 »0.99 >0.95
200 CICS »0.99 »0.95 0.20
PICS »0.99 »0.97 »0.95
TIPI »0.99 »0.99 »0.95
JOINT »0.99 »0.99 »0.95
is most apt to resul t in larger precipitation part.icles It'hich would
survive evaporation losses below cloud base, and therefore result in
larger total rainfall on the ground. The high seeding rate, on the
other hnnd, i!' likely to achieve similar rl1in rates but with smaller
preclpitnting parUctes thnt are mort" vulnerable to evapor;'ltion tosses,
eVE!n though it: prorlu('('s effects in sollie of the l'esponse vtlritltes that
Catl be statlstic,ally recogni;:od with SJn811er somples. 11'1(0 hypothesi;:ed
conservative seeding effect was used to establish an upper lindt on
sa.ple she, should the actual seeding effects be IIUch maIler than
anticipated; it 1l'as also used as a test of the evaluation technique.
14
Based on the results of these simulations for the low (actual)
seeding rate effects, it appeared that SO to 100 samples (25 to 50
seeded, and 2S to SO non-seeded) would be required to reject the null
hypotheses in HIPLEX-l. It was, of course, assumed that the results
for the three response variates used in these sample.size calculations
were indicative of the results that could be expected for all of the
response variates and final test statistics.
4.3 Statistical Evaluation of HIPLEX-l
A statistical evaluation of the HIPLEX-l experiment was carried
out under this contract according to the evaluation plan outlined in
Chapters VI and X and Appendix E of the design document (Interior,
1979). A draft manuscript discussing the Tesul ts of that evaluation
appears as Appendix C to this report; it is being revised for submission
for journal publication.
The evaluation presented in Appendix C is based on the multi­response
permutation procedures (HRPP) discussed in Section 4.1. The
main results of the statistical evaluation of HIPLEX-l are as follows:
1. Pronounced differences were found between the response
variables measured in non-seeded and seeded clouds during
the first 5 min after treatment. Those variables are
associate<! with the initial development of the ice crystal
plumes in tho seeded clouds, and the results tend to con­fim
the initial steps of the HIPLEX-I physical hypothesis
(see Table 2 of Appendix B).
2. Significant differences between non-seeded and seeded cases
generally \I'ere not found in the response variables measured
more than 5 min after treatment. These variables are
associated with the subsequent development of the precipi­tation
in the clouds. Consequently, the experiment was
not successful in following the chain of events of the
physical hypothesis through the subsequent development of
earlier and increased precipitation in the seeded clouds.
However, where differences ,,-ere found (\In ether significant
or not) they were generally in the same sense as suggested
by the hypothesis. One exception was that for the response
variable A~'C8 related to 'tHe behavior of the cloud liquid
water concentration after trcatcent.
The sar.Jple sizes for HIPLEX-l were extremely small (7 Class A-I
clouds, 13 Class B clouds, and no Class A-2 clouds). Therefore. the
absence of significant differences after the S-win mark may well be
due to sample sizes that were not adequate to bring out the differences.
Other possibilities are that there was no seeding effect on the precipi­tation
or that there \I~re some inadequacies in the physical hypothesis.
The latter possibility is supported by the recent work of Super !!. ~
15
(1982). Yet another possibility is that the HIPLEX-l test case clouds
did not eonfol'lll sufficiently well to the conc.eptual situation for tlhich
the physical hypothesis was formulated, in spite of the cloud selection
proceduros employed. In that vein, Cooper et 81. (1981) have indicated
that many of the HIPLEX-l clouds had very s'f\OrITifetimes. which may
have prevented the formation of precipitation in them, lohether seeded
or not. Finally. it is possible that the places and times at \<ihich
the response variables intended to confin the steps in the physical
hypothesis were measured were not chosen correctly for the clouds in
the HIPLEX-l sample. Evidence of earlier developlrent of precipitation
in the seeded Class A-I clouds. and of enhanced precipitation frolll the
seeded Class B clouds, with little evidence of differences consistent
with the inteme<liate steps in the hypothesis, could be taken to support
the latter possibility.
4.4 Final Test Statistics for HIPLEX-I
As defined in the HIPLEX-I design document (Interior, 1979), a
set of final test statistics based on aircraft and radar rainfall
estimates was intended to check the ultiMate steps in the chain of
events of the physical hypothesis. CoIr.parisons of the production of
rainfall fI'01ll seeded and non-seeded cunllus congestus clouds as esti_
I18ted by the cloud physics aircraft and the ground based radar ..."ere
involved. Definitions of these "final test statistics" were aiven on
page 11 of the design do=ent and are repeated here for the record.
Final Test Statistics
1. (a> PCPA
(b) PCPR
2. (a) A'iRA
(b) AVRC
(c) AVRR
Proportion of experimental units that precipitate,
based on the Time to initial E,recipitation at the
+lOC level, .!lrcraft measurement (TIPA).
Proportion of experimental units that precipitate,
~~~d1:ereS~;5t~a~;t~~~ ~:)i~~~;~~~n at the
Average volWl:e of precipitation per experiltenta1
unit, based on Aircraft estimated rainfall at the
+lOC level (AERT. - -
Average volume of precipitation per experimental
unit, based on Radar estilrlated rainfall at the +10C
level, using a ~onstailt Z-R relationship (RERC).
Average volume of precipitation per experimental
unit, based on Radar estimated rainfall at the +lOC
level, Z-R rcla"tionshlp adjusteo by hydroaeteor
measurements (RERA.). -
16
Table 2 presents the final test statistiC$. with point estilaates
and MRPP test resul t5. (AVRR was not calculated because values were
not obtainea for REM.; the reasons for that are discussed in Sec. 5.1.)
The P-values in that table are not based on the NRPP test statistic dis­cussed
in Appendix C. Instead, all the pern.utations of the HIPLEX-l
test cases in each class between non-seeded and seeded treatllents were
eTlUl:lerated and the various ratios indicated in the table were calculated
for each pcn:;utation. The P-values presented then indicate the £Taction
of those pemutations for which the ratio was as favorable (or IIlOrc
so) to the enhancement of precipitation by seeding as the neat:l:lent
allocation realized in the experiment. Unl!er the null hypothesis of
no seeding effect. the expected P-value l«luld therefore be 0.5. and
a Slllall value can be taken as evidence of a seeding effect.
Many of the values of the response variables that entered into
the determination of the final test statistics were default values,
and consequently fe.... of the final test statistics exhibi t significant
results. All the seed/non~seed differences in Table 2 are in the sense
indicated by the HIPLEX-I physical and statistical hypotheses except
that for AVRA (Class A-I). The seed/non-seed ratio for that case is
0.088, but that value is dominated by a single non-seeded test case
(HIPLEX-l Case No.7) and has no statistical significance. The AVRA
(Class B) ratio of 26.!1 has an associated P-value of 0.07S, rot that
result should also be vielo-ed with caution because the ratio is again
dolllinated by a single (seeded) test case (Cue No.9).
SoRe interesting questions are raised by the different proportions
of the test cases that "ere deemed to have produced rain, depeming upon
"nether TIPA (associated with PCPA) or AER (associated with AVRA) is
used to detemine the presence of rain. One IIIOre Class A-I cloud and
three IIOre Class B clouds "'Cre identified as producing precipitation
when AIR was used as the in<!icator. The difference is due to the
1 CD hr- 1 rainfall rate threshold that had to be lIet for TIPA, whereas
no threshold was required for computation of the AER values. On the
other hand, one cloud (HIPLEX-I Case No. 17) produced rain according
to TIPA but had a zero value for AER. In that case, the cloud physics
aircraft observed rain on only one subcloud pass, so the value for the
orthogonal pass that entered as a factor into the calculation for
AER was zero.
According to one response variable or the other, the cloud
physics aircraft observed precipitation from five of the seven Class A~l
clouds, ","hile the radar TIPR and RERC values indicated no precipi-tation
from any of thOll. llo\olCver, for 6 of the A-I test cases no radar
data were available from the +lOC level specified in the design document
and default values had to be used. In the remaining A~l test case (No.6),
both the aircraft and the radar indicated no precipitation. For the
six "default" cases, radar observations taken either at cloud base or
at the lowest elevation angle recorded (see RERB and RERL in Table 6
17
~
~ ~ ~~ ;:, ~
0
~ ~
i=' g .l ~ ~ ..; .; .; ~ N .;
~
;:, ;, ~ 01 5 ;,
e u
~
!t ;, iii g ~ .; ;, .; ;:,
~ s ~ ~ 0 Il .; 0 0
~~ .~ ;, ;, ,. :;, ~ ;,
~. u .;
$0
i:i ~ ;;:e ~ , ~ ~ ;, ~ ~
ou
'5~ ::; ~ ~ " ~ ~
.21 .; .; .;
0 : - ;:, ~ ~ ;:, ~ ~
.e2
l~
i:: 1l -!g<e. ~l . .1 ~ ES ~~ g. ~~ ~ .·3~ .~~ .
H ~ r ~ o.
~~ !~ ~ g ~" ~;
~ go;; t·
~
.i~
,,~ : ~~ ~~ ~~
gl ~ ii ~ ~ l< l< ~
;:e. ~ - . e
S~ ~ N
18
of Appendix B) agreed with the aircraft observations of the presence
(or absence) of precipitation in four. For a fifth Case, the aircraft
TIPA indicated no precipitation, while AER showed a very 51111.11 amount
of rain; the radar data indicated none for that case. The only apparent
disagreelllent betwtl'en the radar and aircraft response variables concerning
the presence of precipitation lo"as for HIPLEX_l case No. 10, and the
8.IIlount of rain measured by the aircraft from that case "ias minuscule
(1 .. 3). Moreover, a radar echo was detected frolll the cloud (lIlaxillUJ:l
z .. 19 dBz) but it was located in the northeast quadrant where radar
beam blockage may have been a problem at low elevation angles.
For the Class B clouds (13 test cases) the aircraft observed
precipitation froll six according to TIPA, or eight according to AER,
According to the pri.J!lary response variables TIPR and RERC used to deter­aine
PCPR and AVRR, respectively, the radar inc!icated precipitation
fron only three of the cases. However, if the additional response
variables RERB or RERL are considered, the radar and aircraft observa~
dons of the presence of precipitation disagreed in only three cases.
Two of them produced only small amounts of rain (at most 0,11 m.m Jon2);
the other was also located in the troublesome northeast quadrant and,
although the RER response variables were all zero, had a ~axilllUli radar
echo of 22 dBl.. For n.'O other cases, the aircraft data indicated
precipitation according to one cri terion (TIPA or AER) but not the
other, \fhUe the radar indicated none, so that the aircraft-radar
agreement was mixed. The rain aIIlOunts for thosc tto'O cases "ere evcn
smaller,
4.5 Results of a Classical Rank Test Applied to HIPLEX-I Test Cases
Table 3 shows the results of applying the Mann-Whitney V-test to
the HIPLEX-l seed and non_sud response variables. He represents the
null hypothesis that no difference exists betKeen the seeded and non­seeded
Slllllples, The direction of the expected response of each
variable is shown in the table as was hypothesized in the design
document (Interior, 1979, p. 12, Table 4). The following symbols
are used:
LR
S
.. sum of ranks of seed cases.
IR
N
'" sum of ranks of non-seed, c;ases.
II .. value of Mann-Whitney V-test statistic.
P(H
O
) .. probability of null hypothesis,
The results of this test can be compared to the univariate MRPP
test results discussed in Sections 4.3, 4,4, and Appendix C. There is
general agreelC.ent concerning the degree of significance of differences
I'
?I ~~~~~~~~~~: ~~ ~~~~~~ :~ ~~
" , 5~5~5S333: ' ::0 55~55~ :~ ,,,,, ::p;
'':';
, , "'i~;;;;1:~d: :=;:; ~~i:;:~ .. ..
,I ;:;;:i::~::;i; :;:;! ~;!:~~~: :~ :e~
.", ~;~~~~~=;!: : ~::: ;::~;~: :~ ::~
~·I ~~~qq~~~~~ :~~ l,.=~= :~ ~~
~ ;.. ~ ., ...."'~~ ... ~~~~ I::: .. ~!:;:::!:::: I!: ~ ,I ~~~;';::;~;J;:~~ :;::;ll ~!:;~;!l~;!l :~ : : ,: : ..
:1'1 ;::~:qU:;:;;:;;:;:: ::1; :;;:::~:::; ::0 ~~
?I ~~~~~~~~~~ :~~ ~~~~q~ :q- : ,,,: ~q ';
~ >0 00..; ........ 0 ....... :"'..;
k :rI ......:: .... - .... .. ~ , .. ..: ~:::::::::;:: ..
!1'
."\ ~~2~2!:::!::::: ::e:: :e::::::::!:: I!::. !!
!!!!!!!i!!R!i ~~~!~!!! !!I!! II i~
ggiimmm~ ~~~nit~ mn '.,
AAA'AA' ... .. J! ~n~mmn~ e!!:eEEEEe ~eeee EE
m~~m Hm i; ;::=
~~~I~!lf~~~!i ['~~Ig~~! mgg gg ~~i,
iimm ~~sn ,. :>]] .. "
I
gog
mmmmW eeeeeeee eEeEe iE ~~I~I iimm ?~H$ ~::! " i~I::1
"':";"';";";';,:"'::"';;"'''' -............ "'~ .. .~ .;~ ... .; ..- ..
20
between the non-seeded and seeded responses. The Sw:lS of the ranks
presented in Table 3 also indicate the senses of the differences.
They show. for eX8Ilple. that AweS in the seeded clouds tended to be
greater than AJIl'C8 in the non-seeded ones. contrary to the HIPLEX-I
physical hypothesis. The senses of the other priJlary responses are
generally consistent rith the physical hypothesis. alt.hough many of
the differences either have little statistical significance or are
alliOst non-edstent.
4.6 Representative DTaw Analysis
Several variables assodated with the HIPLEx-l test cases but not
subject to influence by the seeding were exuined in a search for pos­sible
bias due to a ''bad draw" in the random allocation beb'een the
seed and non-seed treatments. The results, considering the Class A~l
and B clouds combined, are sUltD'larited in Table 4. Some comments
follow:
Time Variables: Time of day and Julian dates of the
test cases were compared bet",een seed and non-seed
cases. Very little difference was found.
b. Seeding Temperatures: The temperatures at which
seeding "'as accoViplished were very close (-10.8C,
seed vs. -10.6C. non-seed). The temperatures were
mensured by the Learjet seeding aircraft.
Sounding Variables: Variables from the 2000 GIT
Milos City sounding were co_pared. AVf'rage values
of surface tCllperature. dew point, low level mois­ture,
lifted index, precipitable water, and wind
shear were very sillilar. There are sOllle indica­tions
of differences in the standard deviations of
the variables, but in vi~ of the small sample
size, these differences probably have little real
significance.
It appears fTOl:!'l these values that confidence can be placed in the
luck of the randomization draw in this experiment. Thus, greater con.
fic.ence can be placed in the statistical results of the experiment.
However, it would be useful to examine the variables measured by the
cloud physics aircraft on the pre-treatment pass (see Table I of
Appendix C) in a similar manner to identify any possible differences
among the individual test case clouds within each class.
4.7 Estimatco:l ~lRPP P-Value [lcpeno:lence on Sample Size for IlIPLr:x-l
To investigate the effect on the P-values for the HH'I,EX-l response
variables if brger slUIlples had been availilble, the existing samples
(4 seeded and 3 non-seeded cnses for Class A~l clouds; 8 seeded and 5
21
ABLE 4: Means and Standard Deviations of "Representat.ive Draw" Variables
Seeded Non-Seeded
Variable ~ ~
!No. of Cases 12 8
~ay of Year Mean (Julian) 182.3 185.0
Std. Dev. (days) 2S 13
ime of Treatment Mean (hr-Qrr) 20.70 20.08
Std. Dev. (hI') 0.93 1.58
Temperature at Meon (OC) -lO.S -10.6
Seeding Altitude Std. Dev. C'C) 1,6 1,1
Radiosonde Variables (2000 GMT)
Surface Temperature Mean (OC) 25.7 26.6
Std. Dev. C'C) 5.' 3.7
Surface Dew Point Nean rOC) 8.2 9 ••
Std. Dev. C'C) 4.1 2.9
Low Level Moisture Mean (g/kg) 6.2 6.7
(SO bPa mean) Std. Dev. (g/kg) 1,' 1.3
Lifting Condensation Level Mean (hPa) 71. 7.7
(using surface T Ii, T
d
) Std. Dev. (hPa) 54 60
Lifted Index ~lean (Oe) -1.3 -1.1
Std. Dev. C'C) 2,2 2.2
Precipitable Water ~:eari (em) 2,01 2.02
Std. Dev. C=) 0,63 0.41
Surface - SOO hPa Windshear Mean (kts) -" _21
22
non-seeded cases for Class B clouds) were doubled and tripled in size
to simulate an extended HIPLEX-I experiMent. The observed values for
selected response variables (PICS, TFE. and AER) "'ere simply replicated
the appropriate nUlllber of times and the resul ts analyzed with the MRPP
univariate test. The results of this investigation (for the raw data
values) are given in Table S.
As anticipated. the P_values become much smaller wi til. the larger
sample sizes. In ItOst instances, strong significance would have been
achieved if the sample size were tripled. That lleans that an extended
experil!ent rith about 60 test cases, which would be at the low end of
the original sample size estimates (see Sec. 4.2), could be expected
to give statistically significant resul ts for llIany of the HIPLEX-l
response variables. The relatively slo,," decrease of the P-values for
TFE in Table 5 appears to be due to the presence of tied no-echo cases
(TFF. "' 2400 s) in both seeded and non-seeded s8Jllples. The aforemen­tioned
60 cases, moreover, would be distributed about 20 in Class A-I
and 40 in Class B, so that significant results are possible for each
cloud class with sample sizes even smaller then the original estimates.
ABLE 5: Changes in MRPP univariate P-values for raw data values if
bserved data sets "'ere doubled and tripled (fOT the specific priJ:1ary
response variables PICS, TFE. and AER)
CLOUD CLASS
~ -'- ~
~
Original 5antple 0.143 0.428 0.289
Doubled Sample 0.113 0.145 0.076
Tripled sample 0.044 0.053 0.021
l!!
Original S8lIlpie 0.486 0.76) 0.505
Doubled Sample 0.276 0.499 0.250
Tripled S8lllple 0.148 0.347 0.135
~
Original Sample 1.000 0.110 0.578
noubled $ample 0.098 0.028 0.286
Tripled S3Jlplc O.02R O.OOR 0.149
23
It should be noted that these results arc based on an extrapolation
of the existing resul ts which are, in turn, dependent on the randomi­zation
realized in the HIPLEX-l experiment, as well as the physical
effects of the seeding. These simulations lI'IUst therefore be viewed
with some caution. For example, the "opposite sense" response of
AWC8 in the existing 20 HIPLEX-l test cases would not be reversed by
replicating the same cases. The AER results for Class A-I clouds in
Table S. although yielding P-values less than 0.1 for doubled or larger
saI1ple shes, are also associated with a sense opposite to that sug­gested
by the physical hypothesis. That is caused by the doIJinance of
one non-seeded test case (~. 7) in the rainfall 8lIIOunts; t.hat case
becomes replicated in the simulated extensions and continues to dominate
the response. Consequently, this simulated extension of HIPLEX-l
merely provides sample size estimates that, because they are based on
data from the actual experiment, should be improvements over the
pre-experiment estiT.lates discussed in Sec. 4.2.
24
S. PHYSICAL INVESTIGATIONS
Various physical studies ..-ere carried out under this cont.ract.
They included both physical evaluations of HIPLEX-I test case results
and studies of clouds not included as part of the fomal HIPLEX-I
randomized seeding experiaent. Mesonet data available f:r'01It the Miles
City area for the 1980 HIPLEX-l period were analyzed extensively.
So.e design studies for a cont~late<.' follow-on cloud seeding experi­Bent
to deal with larger "convective colDplexes" ...-ere also conducted.
Work in these areas is SUDIl'.arized in this section.
S.l Raindrop Size Distributions and Z-R Relationships in HIPLEX-!
As part of HIPLEX-l. the cloud physics aircraft made raindrop
size observations with a Particle Measuring Systems (PMS) OAP-20-P.
two-dimensional, optical array probe in the rain shafts belo",' the test
case clouds. Those observations were used to determine the primary
response variables TIPA and AER. They were also intended for use in
determining Z-R relationships that could be used to calculate the radar
response variable RERA. The observations were made at flight levels
corresponding to a temperature of about +lOC, with typical cloud base
temperatures being about +4C. The particle sizes were determined by
fitting a circle to each particle image in the manner described by
Cooper (1980). These circle-fit data were studied under this contract
to determine SOlie characteristics of the raindrop size distributions
and the Z-R relationships (Smith and Arnesen, 1981; Arnesen, 1982).
5.1.1 Olaracteristics of the data
The 2DwP probe has a sampling VOIUDe of about 1. 7 .3 per kiloJr.eter
of aircraft flight path. The :mage data are accuJ:lulated in a buffer
and transferred to tape when the buffer is filled. Thus the recording
interval, and hence the tir.e (and space) resolution, varies with the
sizes and llUlIIber concentrations of the partieles. In practice, the
number concentration seems to be the dominant factor, with each
''buffer load" typieally containing about 100 particles.
Most of the examples in this section are based on data from
HIPLEX-I Case No.9, which produced the greatest 8l!lount of rain bong
the 20 test cases. For that case, 'the buffer s8l!lpling time intervals
ranged from 0.36 to 48 sec, ...ith a median value of about 1.0 sec.
Corresponding sample volumes vary from 0.07 m3 to 1.75 mS• Thus,
roughly speaking, it is possible to present data for s8ltlple volumes
from around 0.1 mS up, corresponding to resolution along the flight
path from about 0.05 km upwards. The raw samples, ho",oever, are too
small to give accurate estireates of meteorological variables such as
the mass concentration (or "liquid water content") W. the precipita­tion
rete R, or the radar reflectivity factor Z. Consequently, for
many purposes it beeomes necessary to combine the raw samples into
larger composites.
2S
5.1.1 Drop size distributions
Cooper (EISO) noted that the raindrop size distributions from
HIPLEX-l appear to be essentially exponential. Figure I shows a set
of four size distributions, with overlapping sample volumes, that
demonstrates the exponential character of the distributions. The set
was selected to illustrate two lIIain features:
1) The effect of inC-Teasing the sample volUl!t' on the
slIIOothness of the distributions and the apparent
truncation sizes.
2) The need to develop some means of dealing 11'1 th
"outlier" particles.
The curves are plotted using the "inverse CUnJlativc nuJ"ber concentration"
of the particles as employed by Laco (1978; see also Slllith, 1982).
~~ ~:m~~:;a:r~k;D~:~~r::e:~~aih~o~ur1~\~~~e~~~~;0~:~n~~s
abscissa. All the curves are truncated below 0.8 1IIllI, because t.he
slll8:11er particles were not processed by the circle-fit rout.ine.
Consider first Curve ""'0. 1. corresponding to a ra'" sample volume
of 0.200 m3• The sample represented by this curve involved 50 circle­fit
partiCles, a litt.le less than half of the tot.al JlUlllber of particles
observed (the remainder \IIere IIIOstly small part.icles that. were not
processed by the circle-fit program). The distribution is basically
exponent.ial. especially considering the SlIIall salPple size. out to about
2.6 mm. One additional 4.75 .. particle appears on the curve as an
outlier. As t.he sample volUll!e increases (Curves 2. 3. and 4), the
distributions become more nearly exponential. Moreover. the 4.75 mm
outlier particle in CUne I no longer appears to be an outlier with
the larger sample volumes.
The outlier drop contributes about. 50\ of the rain Ill8:SS in the
0.200 m3 s8lllple in Curve 1. It is clear that this one particle
dollJlnates the calculations of W, R. or Z t.o an extent that II8kes the
suple unrepresentative. The use of larger sample volWlles tends to
alleviate the problell to sOlIe extent, but if such a SUlPle were to
be used in analysis work. the outllet: particle should be ollitted.
However, it is not clear how to fOTDllate a procedure for doing this
in an objective manner. Thus, suppose that the outlier were only
4.25 ll\lI: in diameter (or 3.75 or 3.25 or ••• )j at what point. is it. no
longer an outlier? No answer to this question is presently available.
This aspect of the raindrop sampling problem has not been dealt. wi t.h
in the earlier treatments by Cornford (1967). Joss ar.d Waldvogel (1969).
and others.
26
1000~-~--~----r---~-~
200
100
'" 50
'E
B
"":J 20
Z
10
CURVE SYMBOL SAMPLE VOLUME
-,- --- 02001T\3
2 0.820 m3
'3 1.605 m3
4 3.290 m3
050!---L,---2!-----,3!---4L :............J
5
DROP DIAMETER (mm)
~: Four cumulative drop size distributions from HIPLEX-l
~o. 9 (22 July 1979). with overlapping sample volumes.
27
5.1.3 Z-R relationships
To detcI"Illine Z-R relationships for HIPLEX-I fT'Olll the above sort
of drop size data., three issues had to be resolved:
(1) How to combine the ra",· data samples to produce
composite snrnples that can be logitimately
compared on II Z-R $c.atter diagram;
(2) How to fit II relationship to the data points on
the scatter diagral'l; and
(3) How to assess differences Ulong Z-R relationships
for individual test cases. or between seed and
non-seed subgroups.
The first issue relates to the 2D-P probe suplirll procedure discussed
in Section 5.1.1. 'lho raw data samples are generally too SIlall to
proVide satisfactory estimates of R or Z. I-Ioreover. the raw samples
represent greatly varying sample volumes. and tihen they are expressed
in nUl'l'lber of samples per unit of flight path it quickly becomes apparent
that there are many more samples per kilometer in regions of heavy rain
than in regions of light rain.
Two candidate aethods of cOllbining sp.ples were considered in
HIPLEX-I; one method involved combining data for unifoTl! segments of
flight path and the other involved COMbining data for (lllOre or -less)
unifoTIII numbers of particles. The principal argument in favor of
the fomer method is that the segment length can be chosen to match
approxill'.ately the radar resolution. Because the radar observations
represent average values of Z over a contributing region. instead of
average values of R. such a .atch should lead to better radar versus
aircraft collparisons. The principal argm:ent in favor of the 'latter
.ethod is that the uncertainties in R and Z values amputed from a
drop she distribution are functions mainly of the number of particles
in the sample. With unifoTDl numbers of particles in the composite
samples. the reSUlting points on a Z-R scatter diagram should have
roughly comparable uncertainties. The issue as to which method is
preferable has not been resolvec!; the colllposite s8lflJ>les used herein
were prepared according to the "mr.ber of particlu" method (Arnesen.
1982).
The second issue relates to problems with regression analysis.
Three candidate approaches were considered: Ordinary linear regres­sion
on the log-log Z-R scatter plot; linear regression taking account
of the eorrelation between the uncertainties in Z and R values deter­mined
from a drop she distribution (Mueller and Sims. 1966; Cooper
et a1 •• 1981); and me-dian regression (Mielke et al., 1981b). wich
reduces the sensitivity to outlier-type pointS:- Ai'ain, the issue as
28
to which approach is preferable has not been resolved. The results
presented below were obtained using ordinary linear regression, but
t.he advantages of the other methods lIlight well yield significant
illlprovelllents.
The third issue seems to be clearly resolved in favor of using
permutation procedures like IomPP to assess differences in Z.R rela­tionships
among test cases. or between seed and non-seed groups. Any
other approach involves assumptions about the distributions of the
points on the Z-R scatter diagram, in relation to the line of best
fit, that are difficult to substantiate.
The entire HIPLEX-l raindrop data set comprised 372 raw samples,
considering Class A-I and Class B clouds together. The Z-R relation­ship
fit to the points for the raw data snpies was Z • 130 Rl.82..
with a coefficient of determination r2 • 0.64. The composi ting
~~c~~~a~~~~pt::S~~e~3~fR~~l:~i;is.t~.i~~ a~e~~a~:lting
diaa.r8ll for the CODposite drop size data is shOl>"Il. in Fig. 2. Slight
differences ",-ere obtained in each case by perfonring separate
regressions on the seeded and non~seeded groups.
reroarr;:l;"'~i;i~a;c~~t~~~S~i~Sl;~eRt1~ed:;~~;:rf:: :~eO;~~:ization
analysis of radar and rain gage data from North Dakota (Smith et a1.,
1975). A possible explanation for the high eJtponents in theserela­t.
ionships is the coJmllon presence of graupe1 or hail in the showers,
;~~~~h~;~ ~~i~ri~u:~::~~i~fl;o~~:ft~~eZ2~-~3~IT'~f: 3ga~:~d ~e::;':~e
the radar rainfall estiMate RERC in IIIPLEX-l, although for Z > 30 dB:
the difference is within a factor 2.
The difference between points for each individual test case and
the rest of the cases was then assessed by using the NRPP. Pen!Utations
"'"ere determined by allocating the 141 points on the scatt.er diagru
randollly to the case under considerat.ion or the rest of the group. In
brief, the results showed that each individual test case differed
significantly f1'Olll the rest. with P-values as SClall as 10- 5 in soce
instances. However, regression lines fit t.o points for the individual
cases led, as often as nat, to bizarre z..R relationships; the exponent
was 6 in one case and 52 in another. 1h"t leaves us in tho awkward
posit.ion of being able to dmonstrate statistically significant differences
among the points on the l-R scatter diagram for the individual test cases,
while being unable to obtain plausible Z·R relationships on a case-by-case
basis.
Similar comparison of the seeded versus non-seeded groups led to a
sOllooat different quandry. When the MRPP comparison was "one case"
versus "the rest," individual points on the scatter diagrllJD could be
allocated randomly to either "one" or "the rest" to deteTlline the
10
COMPOSITE SAMPLES
x-NO-SEED
--SEED
_.x·
",
2.
E E ,.
w;r
'" ...J
...J
~
Z"
"'I
'0
pel1il.ltations. When the e<mparison to be made was "seeded" versus
"non-seeded", however, the allocation could only be lIlade by placing
all of the points for anyone test case in one group or the other.
The number of HIPLEX-l clouds that produced rain, and therefore yielded
raindrop data. was small; in particular, most of the usable data for
non-seeded clouds came from a single case. Consequently, the number
of possible pennutations was small and no significant P-value was
obtained for the seed verStlS no-seed comparison.
The implications of these results are as follo\lls:
(1) There appear to be significant differences in the
points on the l-R scatter diagraJ!l for individual
HIPLEX-l test cases.
(2) However, satisfactory l-R relationships could not
be deteI'ldne<l for the individual cases from the
data available.
(3) The differences from case to case masked any possible
difference between seeded and non-seeded groups.
Consequently, the only appropriate course of action in HIPLEX-I would
be to use a single overall Z~R relationship in coMputing the radar
rainfall estimates REllA. Whether one of the Z-R relationships presented
earlier is the proper one to use has not been detcnined because of
the unresolved issues mentioned at the beginning of this section.
5.1.4 Colllparisons between aircraft and radar data
It is of interest to compare aircraft observations of rainfall
with radar data for the same precipitation events. ~\ml.erous diffi­culties
arise in making such comparisons; they include problems of
matching the locations and times of the observations, as well as the
vast difference between the sampling volUll:es of the aircraft and radar
data. There is no way to deal completely with the sample volume ques­tion.
but SODe of the difficulties in I:l&tching positions and times can
be cirCUlllvented by comparing line integral values of the reflectivity
factors COV;p.lted along the flight path of the aircraft. That greatly
diJ:linishes uncertainties associated with displacements of data along
the flight path, but unfortunately does not overcome problems associated
with displacements in the perpendicular direction.
For the radar. the line integral I Z·dR. along the aircraft flight
path fOr a pass through the rain shaft can be calculatf'd from tJle
recorded dntn. For the aircraft d:tta, the corresponding quontlt)' is
31
Here C(Di) is the observed nuJIlber of particles of diameter Dp Iffiile
~is1:0 t~ ~a::~~~ ~~:t~~: ~~~~ ~;~~~ ~~~n:~~~ht~~:m;~~ion
interest. SUch a calculation also permts collparing the observations
while cirCUl!Venting any question about how the aircraft data should be
COIIIposited.
One such comparison was attempted by Arnesen (1982). The results
indicated a difference of about a factor 30 if the straightforward
COIllparison "..as made. However, displacing the path of integration by a
distance of the order of 1 km perpendiCUlar to the flight path would
make a substantial difference in the results. Consequently, while the
approach is attractive in principle it proved to have lind ted effec­tiveness
with the small HIPLEX-l clouds. In larger cloud systems
where displacements of the order of a kilometer ,,"'QuId produce smaller
differences in the radar reflectivity factors, the procedure might
work better.
5.2 Studies of Non-Test-Case Clouds
Prior to the official start of the HIPLEX-l experiment in 1979,
cloud physics data sets from 3S clouds studied in 1978 were selected
and examined to aid in the develop~ent of the physical and statistical
hyPOtheses. Cri teria similar to those specified for selecting HlPLEX-1
test case clouds (Interior, 1979) were used to select seeded and non­seeded
cloud samples; these samples were not randomly selected. Of
the 35 clouds, 24 were non-seeded (NS), 9trere seeded (5) with dry ice
at a high rate ('\.1.0 kg bl- 1) and 2 were seeded with dry ice at a
low rate ("I.(J.1 kg bl- 1). Because the T1UJ:Iber of seeded clouds IOaS
small, the high and low rate seeded cases were considered together
as the seeded s3.lllple.
Several microphysical variables were studied, including cloud and
precipitating ice particle concentrations, liquid water concentrations,
and the times to the first appearance of precipitating ice. The vari­ables
were measured at VArious times after treatment (seed tiae, or the
time at which a non-seeded cloud was selected for study) and included:
(1) CIC2 and CICS, cloud ice particle concentrations (1- 1) 2 and S min
after treatment; (2) PICS, PIC8, and PlelO, precipitating ice particle
concentrations (1.-1) 5, 8, and 10 min after treatment; (3) A1\'CS, AWeS,
and AWCIO, cloud liquid water concentrations (g/m S) S, 8, and 10 min
after treatment; and (4) TFPI, the time in minutes following treatment
when the precipitating ice concentration was first greater than or
equal to 0.21- 1 • Comparisons between seedea and non-seeded samples
were made and reported in detail in Dennis;!.!!.:... (1979).
Means, medians, standard deviations, and Mann-Whitney rank test
statistics were generated in a search for differences between ;;eeded
and natural cloud variables. In addition, frequency diagrallls of the
32
cloud physics variables were constructed to help visualize the seed
versus ron-seed samples. Figure.3 compares the changes in the average
liquid water concentrations of seeded and non_seeded clouds with tillle.
This series of histograms sholl's that in 1978. the. seeded clouds tended
to becoJlle depleted of available liqUid water faster and lllore frequently
than the non-seeded clouds. The randomized HIPLEX-l experiment (1979-1980)
did not sho.... siJlli1ar differences between the depletion of liquid water
in seeded and non-seeded clouds. In fact all of the HIPLEX-l test case
clouds had very 10'11 values for AJl'C8 (\.hey would fall in the 10....est
category in Fig. 3) and the indicated seed/non-seed difference was
opposite to that suggested by Fig. 3.
~~ou~;s:~~:sv:~~:~~gv:~~e~~~e~~e~;g:e~~~~idh:=~~:d~o::n~~~~~~:ded
at 0, 5, 8, and 10 min after "treatment" time.
So.e evidence of a tendency for the clouds to dry out rapidly was
present in the 1978 observations. Figure 4 shows a col",parison of the
tilte behavior of the cloud liquid water concentration for seeded and
non~seeded Class A clouds. At "time r.ero," the samples each included
11 clouds. The graph shows only four seeded clouds being sll.l!lpled at
14 min, and no non-seeded clouds. The sampling of clouds in 1978 was
exploratory in nature and thtlS sampling times for individual clouds
varied considerably.
The graph shows a tendency for these small clouds to dry out very
rapidly regardles!l of treatment. This tencency, tlhich has been noticed
in most SlI!all clouds s8l!lpled, suggests that the s8r.pling of the HIPLEX
clouds usually did not occur until after the liquid water concentration
had peaked (at least at the sampling level). This further suggests
that the visual cloud selection criteria used were not adequate to
obtain data over the complete life histories of liquid wat.er
development in most small Bigh Plains cUlnulus clouds.
Examination of similar data for a limited sample of Class B clouds
suggests that, on the whole, they also tend to dry out rapidly, u
reflected in a downward trend in LWC values with tilDe. However, more
frequent occurrences of lIultiple b.Jbbles of rising "'ara, lIIOist air
were observed among the B clouds. This is indicated by IPOre frequent
33
u
'5
w~
cr
~O.51---+J~----+------1
~:wa~;~tc~~c:~~:~~o:n~,~)n~~~ l~;~i:~~ O:~O~~~;~;~i~:SS A
clouds versus time. The liquid water concentration shows a dra.atic
and rapid decrease in these Sll'.all High Plains CUl!lUlus clouds. [}.\1lIIbers
on the curves indicate the f\UlIlbers of clouds remaining in each sample
at the indicated tae after "treatment."]
observations of time oscillations in precipitation particle concentrations
and LWC values in those clouds. That provides a better opportunity for
the subsequent development of precipitation in the Class B clouds.
34
Cloud physics aircraft data from the initial and subsequent cloud
passes were also examined in an attempt to develop relationships for
predictive purposes. These attempts were not t.oo successfUl; details
can be found in Dennis !!. ~ (1979).
Additional studies included a search for outliers in the data
samples. Outliers influence the usefulness of data sets as a predic­tion
tool and decrease the robustness of models being fit to the data.
The cloud variable data sets were also used to explore ways to provide
estimates of missing values for use in the MRPP simulations. Finally,
comparisons ""ere made among clouds seeded wi th dry ice at different
rates. All of the above studies were sUlNlIarized in Dennis et al.
(1979) and a sumnary of these studies was presented at the 1th-ai"n­ferenee
on Inadvertent and Planned Weather Modifieation (Brown and
Miller, 1979).
5.3 Mesoscale Analysis
As a result of various meso-e-seale field programs eondueted in
the 1970's, meteorologists have begun to develop a deeper understanding
of the eoupling meehanisms between synoptie and mesoscale features
along with their interaetion in the development of eonvective elouds.
~lost of the studies dealing with statisties of cases and leading to
short range forecasting techniques have been cardcd out in 1lUFlid
subtropieal or mid-latitude climates. 'I1le Montana HIPLEX mesonetwork
operated during the 1980 summer field experiment provided an excellent
opportunity to develop similar mesoscale analyses for a semi-arid,
mid-latitude cli.Jnate. Analyses of the mesonet data were initiated under
this contract and have been continued with state funding.
The small number of days with vigorous convective activity in the
dry Montana sUllll!'ler of 1980 only allows preliminary conclusions to be
drawn. Studies for five days (1 !-lay, 3 June, 3 July, 19 July and
26 July) ....ith a total of ten independent rain cases were completed
(D::meaud et aI., 1982a; Viswanath, 1982). Two of these days (1 May
and 3 June) were the subjeet of extended studies (Ooneaud at aI.,
1981, 1982b; Miller!!.~ 1981). --
~leasurements from the instrumented surface mesoscale network 10:1 th
25 stations spaeed approximately 20 kJr, apart and from the 5-cm SII'R-75
radar supporting HIPLEX-l in eastern Montana, as lo:e11 as radiosonde
data, synoptic maps, and satellite pictures were used in these studies.
Eaeh mesonet station provided S-min averaged wind, temperature,
precipitation (S min aceumulation), pressure, and relative hun:idity
data.
Systematic error reduction measures were first applied to the
basic mesonet data. Next, an objective analysis scheme using centered
finite divided differences was employed to interpolate the observed
3S
wind velocity data at the mesonet locations and create a regular grid
spacing of 5 km ;lI; 5 km for the horizontal wind components. Every
15 min, fields of wind direction and speed, wind divergence, defol'Wlation.
and vorticity ,,"ere CQSlputed at each grid point. Areal divergence values
:~:sa;~~e~~:t~dxf~~_~a~~~~n~~~~e~~i~~~;;:~~~C~sv~~e=~~~t~~~n~e
surface area of divergence. for magnitudes >6 x 1O-~ 5- 1, and the
spatially averaged wind divergence value over the salte area, at a given
time. Plots of the values on a cell basis and of the variance and
standard deviation of the values for the total network area at 15 min
intervals were produced. Radar Estimated Rain Volume (RERV) was calcu­lated
for each cell using an optTmhed Z-R-relationship (Smith et. aI ••
1975). The tiDe evolution of the areal divergence, the varianceoT"the
net divergence field over the whole net\o'Ork, the lllaXi~ radar reflec·
tivity factor, the total RERV aCCUlllUlations, and other quantities were
analyz;ed for each of the ten rain periods.
The structure of the mesoscale wind fields and their evolution
were found to be some"'ilat different in the dry »:mtana cliMate than
those found in humid climates. Collpared to the humid cliMates, the
areal divergence values in Io!ontana are 8-10 tillles larger. On the
other hand, the rain efficiency (total rainfall divided by total
1IlOisture inflow, and expressed in percent) was found to be less than
for stoms in b.naid cliJ:Iates. The stOl'll efficiency ranged between 2\
and 30\, with an average of 20\. and was lar£er for the larger storms.
A new q\lantity called the Areal Convergence Time Integral (ACTI)
was defined and found to be ",-eIT correlated with The RERV in a semilog
plot (r '" 0.92). The REPV was also found to be "'-ell correlated with
the tiJlle interval between the start of the intensification of the areal
convergence (>6 x 10-4 $-1) prior to the onset of rain and the start
of the rain (r '" 0.96). These facts suggest that the areal divergence
and the ACTI have potential as predictors for the start time of the
rain and t.he total rainfall aroount, respectively.
The variance of the wind divergence field for the whole network
area on each of the five days considered indicated a cyclic evolution.
The duration of the intensification period in the variance of the wind
divergence field, for the cycle occurring just prior to the beginning
of the period of rain, "'"as found to be correlated with the duration of
the rainfall (r'" 0.78). It is important to note, however, that this
was an exploratory study and the results are based on a very lilO'lited
sample she. Additional investigations with further data will be
necessary.
5.4 2O~:~~~~e02a:Pl~;~~:~h~~n~~::~~ini Rainfall fr<lJl!
A study was Ilade of the gaging requirements to measure the rainfall
produced by cloud entities called convective compleJles (Stdth and Cain,
1919). These contiguous c:loud masses, which produce radar echoes
exceeding 30 dBz reflectivity factor and 8.5 bn maximUIII echo height,
are generally larger than the HIPLE)::-l test ease clouds. They were
regarded as candidates fOT future seeding experiments under the HIPLEX
program. Heimbach and Super (1980) and Silveman et a1. (1981)
conducted closely related studies for siJllilar purposeS:-
The study was based on the radar esti.ated rainfall patterns, or
"radar rainswaths," of 256 convective cOlI!plexes identified from the
1977 I-klntana HIPLEX radar data. Those patterns "'ere assumed to repre­sent
the true rainfall distributions. Because we exuined relative
errors in the gage rainfall estill.ates, accuracy in the magmtudes of
the radar rainfall values is not an issue. The resolution of the radar
rainswaths (90,000 points over the surveillance area) is far higher
than could be provided by any feasible gage network.
To estimate the accuracy of gage lIleasurClllents of the rainfall
from the convective complexes, 13 saulated triangular-grid gage net­works
were used to form estimates of the rain volw:e for each complex.
Each grid covered the entire radar surveillance area, and the network
spacings ranged freV! 644 km2/gage to 51 bll2/gage. (I~IeJ:lentation of
these networks would reqtllre fro. 108 to 1344 gages). At each grid
point in a network, gage readings corresponding exactly to the radar
rain amOunts at that point for each complex 'fICre ass\lmed; thus, no
allowance was made for gage eITors. The rain volumes for each com­plex
were estimated by a simple summation procedure equivalent to the
Thiessen polygon technique. These gage estimates ",-ere then coIlpared
to the known radar rain volumes and the relative errors computed.
To deteT1lline the effect of specific gage placement, four replica­tions
(with the network being displaced by a fraction of the gage
separation) ,..ere tested for each network.
5.4.1 SUll:mary of results
Results of the simulation are presented in boll groups, those
related to detection of the convective complexes and those related
to the Ineas~rors. The fonner arc of interest because small
complexes can 1ll1ss every gage in a network. Reliable detection of
complexes having rainswaths sl!laller than 100 b 2 is not practical
because even a net'flOrk with 81 bl2/gage detects only half of these
SIllall co"l!lplexes. COJIplexes with $lOaths larger than 300 iall2 can be
reliably detected by reasonable gage netlOorks.
The resul ts related to .easurerncnt errors were exal~ined in t,,"O
ways. One follows the custom of relating the errors to gage den~ity,
but also considers the effect of rainswath she to obtain further
insight. Those results demonstrtltc that the largest errors occur
with the smallest complexes, regardless of the gage density. This
contradicts the view, sOlf.etimes expressed, that large stoms with high
rainfall gradients represent the IlOSt difficult situation for rainfall
aeasureraents. Accuracies of 50\ or better in .easurernents of rain
"
£1'011 the SDallest complexes (less than 100 b12) cannot be obtained
with any practical gage network. On the other hand. for rainsvaths
larger than 300 kal2• 50\ average accuracy ean be readily obtained and
25\ aCQ.lracy is within reason. Accuracies of 10\ can be achieved only
for very large complexes.
A second way of eXaJ:lining the measurement errors is to relate
them to the nlJJllber of gages receiYi~ rain. As the llUll'ber of gages
measuring rain froll a complex increas..:s. the accuracy of the rain
volUl!.e estimates should improve. Figure 5 shows this behavior; for
the figure. cases ""ere grouped without regard to gage density or
50
"
00!;---L~2}~---'--~4i;----'------'6f-1_-L.--- B
MJMBER OF GAGES RECEIVING RAIN
10
~: Median of the absolute values of the relative erTOrs in gage
esfIiiiih:s of rainfall volumes. as a function of the munber of gages
receiving rain from a complex.
3.
rainswath size. For eXlllIlple. in the si.llulations there ller8 1663
cases where one gage received rain; this T'JJmber includes a mixture
of small co.plexes passing over dense networks and large ones passir.g
ovel: sparse networks. The ordinate in Fig. 5 shows that the median
absolute value of the IIlcasurClllcnt error was Sot for those 1663 cases.
It is surprising that with only a single gage measul'elllcnt. half
of the esti.ll'lated rain volumes can be accurate to 50\ or better. How­ever.
many wildly inaccurate values also occur because the distributions
of relative errors tend to be highly skewed. 'ThE' possible values range
from near -100% to very large positive percentages. Errors of exactly
-100\ are not included because cases where the cOr.lplex missed every
gage were not counted; the largest observed error was +2270\. As Il:Ore
gages receive rain, the distributions becoll\e more nearly s)'ll'J!l:etrical,
and the range of errors is sClaller. With seven or IIlOre aage reports,
the extreme errors in these sil:lUlations were -70\ aoe +114\. The
problem, of course, is that for small COll:plexes (or small watersheds),
a dense network would be needed to insure as lIl8ny as seven gagc
observations.
AnotheT interesting finding is that the rainfall volumes are
strongly correlated with the rainswath areas (Fig. 6). With complexes
spanning sOllIe four orders of magnitude in size, the correlation coeffi_
cient is about 0.95. This suggests that it lOay be possible to determine
the rain volumes by measuring only the rainswath areas. That would
circumvent the necessity for going through a Z-R conversion followed by
space and time integration. Other research (Doneaud et al •• 1981;
Smith et aI., 1982) has shown that inClusion of both "'Kh'i)'area and
duration Illan "area-time integral" (ATl) yields even better estimates
of rain volumes. This approach to the problem of estimatint rain
vollees from convective complexes clearly merits further study.
5.4.2 Principal conclusions
(a) Small cocplexes represent the IDOSt difficult situation for
gage network design. because I!lany of thCI:I Diss all the gages in the
network and the errors in the rain VOlUH estiJ:>&tes for ones that do
not tend to be large.
(b) A convective complex experiment that will include complexes
with rainswaths smaller than about 300 km2 cannot rely on gages alone
for measuring the rain volumes.
(e) Classification of the errors in rain measurements by the
number of gages receiving rain shows that five gage reports may be
sufficient to give median errors of less than 25\.
39
0'0 ......
" ..........
"
100-
0
1
10
1 I
100 103
RAIN$WATH AREA lkm2)
1
10'
~: Scatter diagI1la COllparina radar estimates of rainfall volumes
f'Ci'rCOnvective complexes 'ldth rainswath areas.
5.S Comparison of Gage and Radar MeaSUTelIIents of Rainfall foom
Convectlve Complexes
Because of the problems associated with attempting to measure
rainfall from convective complexes using gages indicated in the pre­ceding
section, any experilllent on convective complexes would probably
have to eMploy radar methods to lleasure the rainfall 8JIIOunts. It is
generally accepted that any prograa for radar .easur_ent of rainfall
should include comparisons between radar and gage estlutes of the
40
rain amounts. However. attempts to devise an operationally satis­factory
method of comparison are often frustrated by the variability
found when the radar and gage estimates of rainfall are compared.
This variability is illustrated and discussed in the present section,
which SUJl1m3rites the results of an examination of some radar and rain
gage data from the 1977 HIPLEX program in Montana (Meli ta, 1982).
Possible causes of the variability include the timing and positioning
errors involved in comparing data from separate sources, variability
in the gage measurements due to effects such as wind or evaporation,
variability in the R~Z relationships, and radar calibration
difficul ties.
5.5.1 Data acquisition and reduction
The radar data for this study were collected with the SIl'R-7S
digital weather radar data system located at Miles City. (It also
proVided the radar rainswath data discussed in Sec. S.4.) It is a
S.4-cm wavelength radar set with antenna beamwidth of 1". The radar
data used consisted of survey scans covering 360" in azimuth, made
at 1" elevation at S-min intervals. The raw radar data. essentially
integrated video signal levels recorded on tape, were converted. to
equivalent radar reflectivity factors. The radar reflectivity factor
was then abstracted for each gage location at each survey scan time.
Those values ....ere converted to rainfall rates using the Marshall­Palmer
relationship Z .. 200 Rl.6 and then integrated over time to
yield the "point" rainfall amounts.
A 109-si te rain gage network was operated in the project area,
with a network density of one gage per 15.5 kJt2 (6 sq mil. Each
site had at least one Belfort recording gage with daily chart rotation
that provided IS-min time resolution and 0.25 rom (0.01 in) quantity
resolution. The basic data are therefore IS-min rainfall totals for
each rain gage location, as measured by the gage and independently by
the radar systEmt.
For this study, the lS-miJl summations of radar estimated rainfall
(R£R) \,,.ere compared with gage estimated rainfall (GER) data at the same
time resolution for four days of interest. One measure of agreement
between GER and RER estimates of rainfall amounts is based upon the
logaritlun of their ratiO, 10g(GER/RER). Among the important charac­teristics
of this "log ratio" is its feature of preserving the sense
of any difference between radar and gage data: positive values corre~
spond to GER greater than RER and negative values to GER smaller than
RER. Ideally, all the log ratios should be zero, indicating perfect
ngreement between GER and RER. It has previously been noted that the
distdbutions of the log ratios tend to be approximately normal, which
cnn be 11 useful property (Cain and Smitll, 1977).
41
5.S.:? Summary of results
Figure 7 compares the frequency distributions of IS-JDin rainfall
allOunts as indicated by the radar and the gages for one particular
day. which is representative of the comparisons. The radar estilllltes
31'e seen to be generally lower than the gage estimates by about a
factor". In vicw of the exponent 1.6 in the l-R relationship used,
this would be equivalent to about a factor 10 discrepancy in the radar
reflectivity factors if the entire difference could be attributed to
radar errors. That is, if the errors were attributed entirely to the
radar data, a discrepancy of about 10 dB would be indicated in the
radar .easuremcnts at that tillie. Other indications suggested possible
radar ealibration errors of the same order of lllagnitude in the 1977
data, but a major evaluation of the radar "as carried oot in the fall
of 1977 (SIIith. 1977) and subsequent data are believed to be IllOre
accurate.
21 JUNE 1977
~
G:i 0.75
~o§
~Q50
§
5°·25 a
°10<. 1Cf3 10-2 IO-l
15 MINUTE RAIN AMOUNT-(INCHES)
~: Comparison of frequency distributions of 1S-min rainfall events
~1 June 1977 as observed by two different methods. GER: gage
estiJllated rainfall a.JUnts. RER: rac:lar estiJllated UIOunts for those
gage locations with non-uTO rainfall.
42
The log ratios \oleTe approximately normally distributed (Fig. 8),
as had been noted fro- earlier studies. The lIean log ratio for the
day (0.437) is consistent with the discrepancy found between the
frequency distributiOns in Fig. 7.
'w"
'~"-O.5 ••••
~ ...
t:)-1.0
g
~'" 2.5
~ 2.0
w
~ 1.5
~ 1.0
~ 0.5
21 JUNE 1977
..,.'
....
.'
-l.bl I 5 20 40 60 80 95 99 99.9
CUMULATIVE PERCENTAGE OF EVENTS
~: Normal probability plot of the log ratios. log(GER!RER), fro.
~ 1977 data.
Besides the differences in the rain llllIOunts. problems were noted
with timing errors. Table 6 swmnarizes the gage and radar data for
the foul' days investigated. Only on 'the day represented in Fig. 7
(21 June 1977) did lllOre than half of the IS-min gage rainfall events
have accompanying radar rainfall amounts to pemit the computation of
the log ratio for that occurrence. Figure 9 illustrates the timing
problems encountered on 13 May; it suggests that a time discrepancy
of an hour or more occuned between the recorded gage and radar data.
The probable reason for this discrepancy is lack of synchronization
between the radar and the rain gage clocks; a network of 109 rain gages
involves 109 independent clocks. and it is very difficult to keep them
accuratel)" synchronized.
l! '- ,.;.!'~ ~~ o§' ~~ .~
l~ S oe, oe, -e oe,
i.:.; .
~ ~~!l
,i ~i ~I .5i
~lq ~q ~~ q~
°e °e o~ o~
.51 ~i ~i ~i
E~ ~S :;::; :a
0C o~ 0C oe.
43
44
16' c--,--,--,--,,--,--,-,-,,--,-,--,
13 MAY 1977
GAGE 6K
~
L't- ~
w~
~
~
~
r---~ER
-
The use of lIesonet stations, with the data transmitted by radio
to a central collecting source. should improve the correspondence of
the timing between radar and gage data in future experiJlents. The
compnrisons could also be made someM111t less sensitive to timing
dhcrepancies hy using Tainfall alIlOlmts accumulated over longer time
periods. Thllt would also lleAn generally larger rainfall fWOUnts for
each "event", 1o'hich could eliminate SOliE" of the difficulties associ3ted
with attempting to lIIeasure very 511.11 8JlOUnts of :rain by either gage
or radar methods.
6. N1Jlo!ERICAL CLOUD KJDELII{; STUDIES
The objective of the numerical modeling effort under this contract
was, simply stated, to simulate 1Illmerically the HIPLEX-I field experiment.
To accomplish this objective, a two-diJl:ensional, slab-s)'JllDletric, tille·
dependent convective cloud model dubbed "SUPER HIPLeX" was used extensively.
The .cdel vas .edified and improved to increase its realisll and to Illiaic,
to a considerable extent, the field Oferations. Nine distinct efforts
were undertaken to tlOdify and update the model:
1. Add a snow content field to the rode!.
2. Improve the random perturbation scheme of temperature
and water vapor for initiating cloud development.
3. Add convergence-divergence to induce cloud formation
when convective cells otherwise fail to reach the
condensation level.
4. Develop a capability for siJ'.ulating dry ice seeding.
S. Add air density effects to the computations of tenlinal
fall velocities of rain and hail.
6. Achieve a better simulation of mel ting for tht, gTaupel/hail
field.
7. Develop cross-sectional output products for comparisons
with data froll aircraft penetrations of the clouds.
8. Vect:orize the code for illproved exeeution on the
CRAY-I computer.
9. Improve the rodel side boundary conditions.
This section discusses several of these developments in some detail.
The basic cloud model has been applied to simulate all of the
1~79-80 HIPLf.X-I test cases, in both non-seeded and dry-icc-seeded
versions. So1:le other HIPLEX clouds were also sil!l.1lated. Several
studies using I:.odel results were accomplished during the contract
period. They include the follorlng:
1. Effects of time-step variations on model results.
2. AgI and dry ice seeding effects on the dynamics
and microphysics of High Plains clouds.
3. Aircraft versus model data comparisons.
4. Convective precipitation forecasting.
5. Case study compari sons.
Sollie of the rewlts of theso studies arl:! suaaarized in bter subsections.
46
6.1 Addition of a Snow Field to the Model
The basic two-dblensional. time-dependent (2D'ID) lI.Il2.erical cloud
llOdel of Orville and Kopp (1977) .-as modified to include snow as an
additional fona of precipi tacing ice particles. The inclusion of snow
allows for an intem.ediate and distinct entity between the two {oms of
ice previously modeled, naDlely. the non-precipit:ating cloud ice (ice
crystals) and the precipitating ice (graupel and hail). That results
in a IIOre physically sound representat.ion of ice processes in general,
and, in particular, of the production of hail.
The resulting model, described in Lin et a1. (1982). uses the
''bulk water" microphysical parameterizationteCliii"ique to represent the
precipitation fields (rain. snow. antl_ hail). All are assur;:ed to follo1o'
inverse exponential particle size distribution functions. Autoconver~
sion concepts are used to parameterize the collision·coalescence and
collision-aggregation processes.
An assortment of accretion processes involving the various fonns
of liquid and solid hydrometeors are simulated in this model. The
transfonnation of cloud ice to snow through aggregation and Bergeron
processes and the subsequent accretional gro\rl'tb or aggregation to fon
hail are simulated. Hail is also produced by various contact freezing
mechaniSlls and via probabilistic freezing of raindrops. Evaporation
(sublimation) is considered for all precipitation particles ouuide
the cloud. The melting of hail and snow to fonn rain is included in
the model. with wet and dry growth of hail and shedding of rain from
wet and lIlelting hail also siJIulated.
The influence of the inclusion of snow in the model was evaluated
by collparing model outputs for three cases: (1) with all IlicrophysiCal
processes active; (2) with the snow processes prohibited; and (3) with
all processes except rain fOT'lll8tion by autoconversion active. The
first two cases indicated siJIilar cloud evolution Q.l.e to the strong
influence of the early formation of hail developing from frozen-drop
elftbryos. The third case. while initially less efficient in producing
bail (graupe1 eIIbTyos). resulted in higher precipitation intensity and
stronger downdrafts. In all cases. DIOSt of the hdl melted to rain
before reaching the ground; the final case producod the Il"Dst hail at
the surface. The presence of snow Iqwers the mass concentrations of
ice crystals, and virga from cloud anvils now appears in the model
outputs.
6.2 Addition of Convergence Effects to the Model
A study was conducted to investigate the effects of mesoscale
convergence or divergence on cloud convection (Chen and Orville, 1980).
The cloud model used was the two-dimensional, tillie-dependent model
with water vapor, cloud water. rainwater, cloud ice. and hail fields
but without the snow field. The lIIOdel was ron on b,-o representative
"
soundings for stol1llS which occurred over the HIPLEX area. The first
sounding was unstable. while the second was conditionally unstable with
a low-level inversion.
The second sounding had a shallow moist boundary layer near the
surface. capped by the temperature inversion. Dlring a period of only
30 llIin, the superimposed mesoscale convergence of IO-1t $-1 "..eakened
the temperature inversion significantly. Also, the air column fro.
the surface to 500 hl'a was moistened 1.y the convergence field. The
moistening rate was ....18\ per hour. These two changes in the atDo­spheric
sounding played an important role in triggering active cloud
convection.
Random impulses and a single impUlse were used in separate rons
for the unstable HIPLEX sounding to 1mtlate convection. The results
sholo-ed that clouds in the convergence case have deeper and broader
feablres than those in the non-convergence and divergence cases.
Furthc:n:J:lre, a power spectrum analysis showed that the ~xiU\lD. flux
contributions shifted toward larger size eddies in the convergence
case. This suggests that the SlIall eddies were joined together by
the superimposed convergence flow field.
The results suggest that to effectively forecast cloud scale
convection 3-6 hr in advance, some knowledge of the mesoscale con­vergence
field will be needed, particularly if severe stoms are
expected. A relatively stable and easily applied IDethod. of super­imposing
mesoscale convergence fields on a cloud-scale IIOdel has
been dsonstrated and could be used in a predictive cloud lIOdel.
This capability has been CIllployed in Ilany of the siaalations
discussed in later subsections.
6.3 Time-Step Effects in the ~k>del Results
In the process of simulating the HIPLEX-I dry ice cloud seeding
experiments (see Sec. 6.6), an effect of changing the model time step
came to light (Orville and Hirsch, 1981). It appears that the model
results are sanewhat time-step dependent. even though a ti.Be step is
chosen that aaintains ro.erical stability. These results are
consistent with "'lin-Nielsen's work (1979) on larger scale IIOdels.
A time-step change is required in the model lihen dry ice is
introduced into a moderate-sized model cloud. The dry ice pellets
fall at speeds of 20 m s-1 or greater, while the model wind speeds
may be less than 10 m s-1. The time step required depends on the
largest velocity in the domain. Consequently, an automatic reduction
(often a halving) of the time step will often occur at the tac the
dry ice is introduced in the lIIOdel dOllain. Thfl clouds in TUns with
<.Ii ({creflt tilDe steps would subsequently devdop in a soM",tlat different
fnshion, even 1f no dry icc rt:'1t:nse \llCre siltlulatcd. Consequently.
comparing a seeded version and a non-seeded version (the two versions
having different tille steps) I:l8y show seIDe spurious seeding effects.
48
The lesson to be learned is that cloud seeding simulations should
use the same time steps as the non-seede<! simulations if comparisons
are going to be made between them. Seeding sioolations for silver
iodide smokes will not encounter this problem because the nucleant
particles are assumed to travel with the airflow.
6.4 Simulation of Silver Iodide Seeding in the ~Iodel
Hsic et 81. (1980) reported the development of a capability for
simulating~ce:phase convective cloud seeding using silver iodide in
the two-dimensional. time-dependent cloud modeL An appropriate field
for representing the distribution of the seeding agent along nth a
conservation equation and associated physical effects for the seeding
agent were added. The agent generates ice crystals via contact freezing
(inertial impact and Brownian motion) and deposition (and sorption)
nUCleation. The vast majoTity of the seeding agent was activated by
deposition nucleation.
For the three soundings considered, a total of eight simulated
(cloud base) seeding experiments were conducted. Six of them were
devoted to one primary sounding, for which the location, amount, and
time of seeding were varied in different cases. The effects of vari­ability
in natural ice nucleus concentrations were also studied. The
availability of the seeding opportunity, or "time window" of the
natural icing process, is related to the concentration of natural
ice nuclei and the flo\ol pattern.
This study showed the potential to augment precipitation by AgI
seeding. The specific response was dependent on the location, time,
and amount of seeding as well as the cloud circulation, because
advection dominates turbulent mixing in the transport of the
seeding agent.
6.S Dynamic and Microphysical Effects of Silver Iodide Seeding
Orville and Chen (1982) attempted to separate the dynamic and
microphysical effects due to cloud seeding through model simulations.
In this study, the 2D'ID cloud model described by Lin et al. (1982) was
used to simulate the effects of silver iodide seeding"l'aSTn Hsie et
al., 1980) on vigorous convective clouds produced with a High FlaiM
sounding. A method of comparing differences among the results from
different model runs with various physical effects turned on and off
was used to illustrate the overall seeding effects. That approach
was also use<! to separate those portions of the effects of releasing
latent heat of fusion and of water loading Io,nich are due solely to
the ico-phase cloud seeding.
In general, th~ loading was fOUlld to be of greater dynamic
consequence than the release of latent heat of fusion, for both natural
and seeded clouds. On the other hand, the latent heat of fusion
49
exhibits a stronger seeding effect than does the loading. The results
indicated siiTIificant effects from both latent heat and loading due to
seeding, but only at 10 min or so after seeding when the glaciation
is being accoll!P1ished via accretional freeting of cloud water by pre­cipitation.
Direct glaciation by the seeding of this vi&orous cloud
did not: occur within a minut.e or so of the seeding time.
Several cycles of cloud growth were indicated for both the natural
and seeded versions, with the timing of precipitation and the trajectory
of its fallout having a pronounced IIlOdulating effect on the stOI'll inten­sity.
For the sounding considered, earlier predpitation (onlation
and fallout. in the seeded versions resulted in a decrease in the intensity
of the subsequent storm developlIIent.
~lore details of the results of this study appear in an ~1.S. thesis
by Chen (1981) that has given us much insight into the physics of the
seeding process. The study fSIphasi:z.ed the Ilany interactions that aay
occur lU!Ong the cloud arv! precipitation particles and their influence
on the cloud circulation. It also shoved that interactions of one cloud
cell wit.h another via the release of precipitation froll. one cell into
another can be extremely important to the organization and life cycle
of the ''parent'' stom system.
A few of the pritJat')' results of Chen's study are SUJllldrizecl below.
(a) Cloud seeding wit.h silver iodide hastens the glaciat.ion and
increases the kinetic energy and development of the seeded cell (for
the first cycle cloud).
(b) The cloud system evolution is accelerated by cloud seeding.
Three cycles of clouds "ere identified in the non-seeded version, while
four cycles are evident in the seeded version.
(c) Cloud seeding may cause precipitation to occur several
minutes earlier.
(d) The non-seeded cloud ~was more vigorous in this case.
Development in the seeded cloud system after an init.ial te~rat')'
grovth surge was not as vigorous.
(e) Cloud seeding with this "HIP-3" sounding resulted in a
36\ decrease in the aCCUlll.llated rainfall tIlIlount at 60 min after
treatment, compared with the non-seeded version.
(f) The dyn3lJlic seeding hyPothesis and related chain of events
were not borne out in this numerical simulation. A IlDre COlllplex
situation occurs in the siMulation, and the timing of events (such
as precipitation fonnation) influences the seeded IIOdel cloud in a
destructive fashion.
so
Separate effects of latent heat of fusion and condensate loading
on the eloud dynamics include:
Ca) Freezing via accretion of liquid water by ice particles and
through the Bergeron effect was more effective than direct glaciation
of the cloud water in this vigorous IIIOdel cloud. Thus the latent heat
of fusion effect becomes significant only when "indirect" freeting
takes place.
(b) The loading effect is directly proportional to the weight
of the condensate, and the cloud water loading plays a rore important
role in the cloud growth than the precipitation particle loading.
(e) The loading effect suppresses the u~ard I:IOt10n and causes
the precipitation to reach the ground earlier. Cloud evolution
therefore is accelerated by the loading effect.
(d) The loading effect is mlch !rore important for cloud gyowth
than the latent heat of fusion effect, because the fOI7.er exists
ll'henever condensate exists and the latter only lihen freezing occurs.
Latent heat of fusion and condensate loading effects due to
ice-phase cloud seeding include:
Ca) Cloud seeding hastens the glaciation and induces earl ier
release of the latent heat of fusion. The timing of this release is
important to the circulation pattern, as well as to the circulation
strength.
Cb) The somewhat stronger upward motion found in the seeded cloud
at 2 to S lIin after seeding is mainly due to the release of latent heat
of fusion from the glaciation of cloud water. HOlo'(lver. this direct
freezing is slow relative to the growth rate of the cloud. and the
induced latent heat effects are negligible in relation to the overall
seeding effect.
Cc) Substantial accretional free:r.ing occurs about 10 llin after
seeding in this HIP-3 sounding case. ibis "indirect" freezing has GlOre
effect than the direct freeZing of the cloud water. The release of
latent heat of fusion at this stage causes a tell!perature increase of
2C and results in a 3 m s-1 vertical velocity increase in 3 Illin.
Cd) The extra loading due to the additional condensate caused by
seeding is negligible compared to the overall loading effect. However,
the redistribution caused by earlier precipitation formation results
in a signficant change in cloud cell interactions, lo"hich is crucial to
the cloud groll-1:h and the total amount of precipitation in this case.
51
6.6 Simulation of Dry Ice Seeding in the Model
Sirolation of dry ice seeding in the Ilodel is accomplished by
InltlaUdng a field of dry icc at a few grid points at a specified
location within the simulated cloud. The center point. of the initial
dry ice field is specified to represent where the agent _lght be
released fran a seeding aircraft.
Parameters control the horizontal and vertical extent of the initial
dry ice distribution. The concentration of the dry ice in the core has
a constant value that may be limited to as little as one grid point or
may extend vertically or horhontally over several grid points. CUtside
the core region, the dry ice Ilixing ratio decays exponentially wit.h
distance. At the first grid point outside the core, the concentration
is 13.S\ of the core value; at the second grid point 1.8\; aPd 0 beyond
that.
Initially the core of the dry ice region was spread for these
simulations over three vertical grid points (0.6 km) and one horizontal
plus the "decay" grid points. Once activated, the evolution of the
dry ice field is controlled by sublimation, the teninal velocity of
dry ice pellets, and advection. 11Ie CO2 then descends through the
IIlOdel cloud, sublill!i~ as it falls.
Sublimation of the dry ice results in the fonaation of cloud ice
crystals in the model clouds, with lOll crystals fomed per gram of
dry ice sublimed. Natural ice crystals also fon with concentrations
increasing exponentially with decreasing tell'lperature (Fletcher, 1962).
At -2OC, one natural ice crystal per liter is assumed to form. Cloud
ice which is fOIl:led (whether by the dry ice or naturally) grows by
vapor deposition and interacts with cloud liquid by riJIing until it
reaches precipitation size (snow). The snow interacts with the cloud
liquid and cloud ice to fona hail (primarily graupel). Rain can form
fro. the melting of the ice particles and/or the shedding of cloud
liquid frOJll hail. These cloud microphysical processes are described
in Lin et al. (1982). Orville and Kopp (1977), and Wisner et a1.
(1972).-- --
The llOdel was nm on a HIPLEX-l soonding fro-. 22 June 1979, and
the resul ts were included in lapp et al. (1982). Cloods of both
Cass A-I (non-seeded) and B (seedilJ'}"""'OCcurred on this day. Several
clouds formed in the model simulation, and the one most central to the
grid was seeded. Both a seeded version and a natural (non-seeded)
version were simulated. Cloud ice foned earlier in the seeded version
than in the non-seeded version as a result of the dry ice seeding. That
behavior is consistent with the HIPLEX-l physical hypothesis.
Precipitation began earlier, resulting in a longer period of
precipitation, in the seeded version colllpared to the non-secd~ ver­sion.
Figure 10 compares the accW'lUlated rain as a function of tiMe
52
24~~~~~~~~~~~~~~~~
22
20
_18
E Sl6
"14 z
212
SID 0: 8e
0:
"-6
~: The accumulated rainfall vs. tae since ~el initialization
1i1tlieseed and non-seed versions; units are kilotons of ...-ater per
unit length in the y-direction in the llOdel.
in the seeded and non-seeded versions. The rainfall fl'Olll the first cell
accounts for the first 10 }(T/bb (from 68 !Din to about 81 min of model
til:le) in the seeded version, and that from the second cell for the
final 14 kT/km. The two cells are not as distinct in the non-seeded
version. The rainfall acc\1tlulation in the non-seeded version lags that
in the seeded version by about 4 min, and is less by about 20\. Those
resul ts are again consistent with the HIPLEX-I physical hypothesis.
However. the model clouds 'fIere found to be wetter and developed
precipHation faster than the actual clouds observed on that day.
6.7 Simulation of HIPLEX-l Test Cases
The modifications and additions to the IllOdel discussed previously
were made largely in order to silllUlate the HIPLEX-I seeding experillents.
53
Simulations have been run for all test case days from the 1979 and 1980
field seasons. Both non-seeded and seeded versions of the JIlOdel for
each day were run.
Atn:ospheric sounding data Io.'ere received from both the Miles City
and Baker HIPLEX radiosonde sites. together with aircraft ascent data,
for the 20 test cases of 1979 and 1980. A representative sounding for
each test case day was used as the basic input data for the numerical
cloud model runs, but additional input data were required to "tune" the
model for each test case. Those data included the surface heating,
the presence or absence of precipitating ice, and the presence or
absence of cloud ice at the cloud top. The cloud microphysical data
were taken from the cloud physics aircraft observations.
The SUPER HIPLEX model was run on the CRAY-I computer at NCAR,
with the input data specified, to generate a cloud that simulated the
test case. Once a non-seeded cleud was simulated, the time and position
of the cloud as it grew through the -IDC level was noted. That time
and position determined the appropriate location and time for the
simulated release of dry ice. Then a separate seeded version of the
model was run. Consequently the model outputs include results for
both seeded and non-seeded versions of each test case, whereas only
one version or the other is available from the actual experiment.
The numerical cloud model output was modified to include horizontal
profiles through the domain at selected heights. A maximum of five
profiles can be produced at any output time. These profiles are
intended to correspond with aircraft traverses through a test case
cloud. Figure 11 illustrates a model cloud and sho,,'s the level of pene­tration
of the cloud physics aircraft at (t .. 4.9 min),t being the time
of treatment. Figure 12 shows the state variables and ,,'ind speed at
that time and altitude as a fUJ1ctien of horizontal position across the
domain. The cloud microphysical variables also available in this form
include the cloud water, rainwater, snow, and hail mass concentrations.
Number concentrations of particles greater than 200 and 600 11m in
diameter correspond directly to HIPLEX-I primary and secondary response
variables that were measured by the cloud physics aircraft.
Using plots such as these, differences between seeded and non-seeded
numerical simulations can be evaluated to help interpret the differences
between seeded and nen-seeded clouds. Furthermore, by introducing vari­ables
from the non~seoded simulations as predictors for both the
seeded and non-seeded test cases, the power of statistical tests for
the existence of seeding effects may be increased. Finally, the model
outputs prOVide a complete set of comparable seeded and non-secded
versions for each test case, something that is not available in the
actual HIPI.EX-I data. That permits a IIlOre direct evaluation of seeding
effects with the model rcsults.
54
-- --- 7
f--' / '\
°O~L-~L-!-'"--;6~L-,8!-'--,!I0~'--;!12~--,J14:-,--,J16:-,--,J'8l,--.!l
x-DISTANCE (kmr-
~: Hl..EI.erica.l siculation at 72 !lin model tille of HIPLU-l Test
case No. 10. 23 July 1979. This was a Class A-I cloud. The solid
lines bound areas of 100\ relative hucidity; the S's indicate the
appearanCe of snow concentration greater than 0.5 g kg-to The
dashed lines are streamlines, and the dash-dot line represents the
second cloud penetration of the cloud physics aircraft.
6.8 Comparison of Model Outputs with Actual HIPLEX-l Observations
From the IIOdcl results, cross sections of many of the cloud state
variables (temperature. vertical Velocity. potential and equiValent
potential temperature) al'd microphysical variables (cloud liquid water
concentration. cloud ice concentration, snow, hail/graupel. and rain
concentrations) "ere produced at the aircraft flight levels for specific
Uaes after tnament. Hence, many of the HIPLEX-l prilllary and secondary
response variables are also available froc the <:.loud model outputs. The
following remarks and figures give slllJlples of what is available and the
results of a few comparisons. (lolore extensive COIl!parisons and sta'tis'tical
tests are planned for all 12 test cases from 1979 and the 8 test cases
of 1980). The HIPLEX~1 response variables are defined in Appendix B.
Cross sections like those shown in Fig. 12 can be used to obtain
these response variables from the model outputs. Unfortunately, the
levels for the cross sections shown here for the first case (22 June
1979) were 1111 below the fonnution levt'l of the maximum cloud ice and
SIlOW 1n the model cloud. That. provi<lcs a further indicaUon that the
levels (or times) at which the response varinhles were W1easured in
IIII'LEX-I lII&y not alW8)·s have becn tile IlIOSt appropriote for checking
~
oz""
55
ML 79072320 23JULYI979 UWY2 Al C NOSEED HIP7910D
8 STATE VARIABLES AT Z~ 4.4km,T:72.D mi
~ :2o
-2 -. -6
!~~~I]
53~ii~1 _ 535.84
1~~~
~ 535.78
w 53576
g: ;;~~
535700 2 4 6 8 K> 12 14 16 18 20
DISTANCE FROM LEFT BOUNDARY (km)
~: Profiles of state variables and wind components across cloud
~in at height 4.4 b:!. after 72 lIIin of silmlated tillle. Hori­zontal
and vertical ldnds (U and W). temperature, and pressure are
shown.
th~ physical hypothesis. Nevertheless. values for the various response
variables can be calculated from these cross sections and they do show
differences between the seeded and non-seeded versions (but not the
lIlaximull differences).
Figure 134 shows an example of the simulated cloud physics data from
the aode! output for the 22 June 1979 sounding. The snow mass concentration
(g .-3) and the ItUIllber concentrations of particles larger than 200 lim
diameter (~.t-l) and larger than 600 \.1m diameter (lte l ) are plotted
across the morlel domain at 57 min of model tilJ:e and at 3.8 btl above
ground level. At 4.8 kIn altitude. the values would be about 100 times
grellter. those samples corresponding more closely to the middle of
the cell. Th" growth of the model cloud pushed the IIItlld~\um concen­trations
of snow and cloud icc above the -8C level specified for the
cloud physics aircraft penetration in this instance.
The clouc: liquid water concentration (LWC), cloud ice mass
concentration and vertical velocity values are shown in Fig. 13b. The
LWC value of >2.0 g m- 3 is higher than the observed values for the test
case clouds on that day. The CIC5 value is obtained by taking the ice
mass concentration (IKC) from the lower curve and converting it to a
number concentration by assUDling an average size for the ice crystals
(10 )lm).
The stnte variables shown in Fig. 13(' give the temperature
variation through the cloud, as """ell as the velocity and pressure
variations. Other curves are available in the model printout for the
hail and rain mass concentration fields.
Table 7 shows a few of the HIPLEX-I response variables obtained
from model and aircraft observations for this case. Generally the
model cloud microphysical results arc lower than the observations
taken at the aircraft sampling altitudes. (But, as noted above,
higher values were present at higher altitudes in the 1I'.0del clouds.)
The times to first radar echo and first precipitating ice are shorter
in the model results than those observed in the field. The non-seeded
cloud actually studied never did reach a precipitation stage. but the
corresponding model cloud deVeloped precipitation at about 14 min
after treatment.
Thi s technique for simulating dry ice seeding of cumulus clouds
produced reasonable results for this test case. Model clouds formed
wi th relatively cool bases at about 2 Ian above ground level and developed
to a maximum height of about 6 Jon in the first surge. and to near 8 btl
in a second growth surge. The model clouds were not completely isolated,
so that the rain production depended on the interaction of one cell
with another. The seeded version exhibited stronger interaction of
one cell with another, because of the earlier formation of precipitation
in the seeded cloud. The resulting precipitation from the two cells
was about 20% more in the seeded version.
The model clouds were wetter and developed precipitation faster
than the actual clouds, possibly due to several items inherent in the
simulation. The actual clouds were generally shorter-lived and had
lower liquid I"ater concentrations. The specified initial conditions.
the eddy mixing coefficients. two-dimensionality of the model. or other
factors (known and unknown) may contribute to the differences between
the model and the actual clouds. Model resul ts for some days agree
57
!~r--- r
Fi'S/3: Simulated aircraft sample of clouds taken 3.8 bII above ground
at min of model tille. or about 5 -.in after treatment ti.e. (a) Snow
variables; (b) cloud variables: and (e) state variables. See text for
addi tional explanation.
58
§ ~Ii 0
:0; ~ ::; g
~
::I~ ~
~ i: ~ :0; ::; g
" ~I ~ 0
i': .!'. :ci :0; g
~ ~11
~
~ :0; ~
~ SII; 0 f 0 ,; 0 ,;
g ~Ij .~
<J s; ~ - ,;
1 ~I"" :g 0 :g ~ ~ ,; ,; ,; ,;
~ fllf is
1l u ~ ,; ~ 0 0
~!
~I"" :g u, ,; 0 ,;
"il U ~ ~ a NI"" 0 0
~ c~ 0 N ,; ,;
.~
"il E
~
il' ~ ]~
8 ] ~I j~~ N ~
~
:l "" e
59
better with the observations than do others. sets of seeded versus
non-seeded /IOdel results, and seeded (model) versus seeded (observed)
and non-seeded (model) versus non-seeded (observed) results, can be
tabulated to make more detailed comparisons of the differences.
In situ airttaft measurements of another HIPLEX-I test case (Case
No. Ilrf'rOil'"23 July 1979) were also cor.pared with results from the
SUPER IIIPLEX model ()liller et al., 1981). The initial convective
tower selected by the aircrattcrew passed its pre-treatment selection
criteria and was subsequently seeded with dry ice pellets dropped into
the top by the jet seeder aircraft. Subsequent cloud physics ~easure­JIlcnts
showed increased ice particle concentrations, a rapid decline
in the cloud liquid "'ater concentration (Lit'C) • and early to~r dissi­pation.
A new tower just northwest of the initial cloud ""as subsequently
penetrated as part of the same test case, as it was attached to, and
a part of, the seeded aren of interest. Thus a teJllporary increase
OCCUlTed in the liquid water concentration ..easured about 11 min after
cloud treat&ent.
'lhe initial cloud measured 3.1 m in depth and 3.1 m in width at
the time of selection. The selection time was the time when the cloud
top passed through the -ICC level. This compares with the 3.5 Ian
depth and 2.4 b width as indicated by the cloud model at near selection
time (cloud DOdel tillle of 66 .. in). (A point to reste.ber is that nothing
can be said about the dimension of the cloud in the y-direction due to
the b'o-dimensionality of the model.)
The cloud II\Odel indicated a total of three cells associated with
this case. A second cloud developed to the left side

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Report 82-7
RfSE;';:'f'J! ON EVOLVI~ resIGN AND EVAWATION OF
mE HIPLE:X PROGRAJ>l: FIP\AL !EOOICAL REPORT
By: P. L. :::aith, P. w. lo!if!lke, Jr•• • K. J. Berry:
A. A. foneaud, R. D. Farley, J. H. Hirsch,
P. J. J."opp, J. R. Miller, Jr •• H. D. Orville.
and D. L. Priegnit%
Rovember 1982
Prepared for:
Division of Atmospheric Resources Research
Bureau of Reclamation
U.S. Oepartment of the Interior
Box 25007, Denver Federal Center Contract No. 8~07-83~V0009
Denver, CO 80225 dated 15 December 1977
Institute of Atmospheric SCiences
South Dakota School of Mines and Technology
Rapid City, South Dakota 57701
·Colorado State University. Fort Collins. CO 80523.
=::~-:~-"l""
,. REPORT NO.
Insti tute of A.tlJOspheric Sciences
S.D. School of Mines and Technology
Rapid City, SD 57701
·D\"v°iN:~~ri."oAr~f.rix,N;p'Yic"r"fc ~eRs~~rces Research
Bureau of Reclamation
U.S. Deparwent of the Interior
Box 2500~;" D:~~~~ Federal Center
8-07-83-VOOO9
Final Report
Dec 1977 - Nov 1982
Subcontractor _ Colorado State University. Fort Collins, CO 80523
This report summarhes five years of research related to the design,
conduct, and evaluation of the U.S. Bureau of Recllllllation's HIPLEX progran
Most of this research concerned the IIlPLEX-I experilllent that involved
randomhed seeding of small "lontana cUliulus congestus clouds with 'dry ice.
The report discusses the design, conduct, and response variables of
UIPLEX-I and presents a statistical evaluation of the experiaent. Ie also
surlllllarizes the results of related physical, statistical, and nUll:erical
cloud JIOdeling studies. The physical studies included analyses of HIPLEX
aircraft, mesonet, radar, and rain gage data. The sutistical investi­gations
were concerned uinly with the deve10JDent and application of the
wIti-response pertlUt;ation procedures (MRPP) used for the statistical
evaluation of HIPLEX-l. The numerical r=odeling studies included
silllUlations of each of the HIPLEX-I test cases.
'7. N~V WORoS ANO OO1.:"
"", .,;.'-
-f-j '(n 'I
·f,; 1'::1--
-f
i ' ,,\-. 1
;'.;
,-j 1,>
,,- to.:
,6
.f' \f-f;;
i,:i!'
'; ~1
i'l :,;
.~. (
TABLE OF CONTENTS
ABSTRACT ..•••••
LIST OF FIGURES •••
iii
LIST OF TABLES • • • • •
1. I/IITRODUCTION .••
2. BACKGROUND: OVERVIElI' OF llIE HIPLEX PROGR,AN ••
3. THE DESIGN AND CONDUCT Or HIPLEX-I ••••••
3.1 The Randomhation Procedure ••.••••
3.2 Boxing of the Radar Echoes for Test Case Clouds •
3.3 Values for the HIPLEX-l Response Variables ••
3.4 Checks of Values for the HIPLEX-l Response
Variables •••
3.4.1 Radar. • • •
3.4.2 Aircraft •••••••••••••••
vi
4. STATISTICAL STUDIES •••••••••••••••••
4.1 Development of ~tulti-Response PeI'1llUtation
Procedures (MRPP) • • • • • • • . • • • • • • 9
4.2 Prelillinary Sample Site Estiaates for HIPLEX-l • 10
4.3 Statist.ical Evaluation of lUPLEX-l • • • • • • • • 14
4.4 Final Test. Statistics for HIPLEX-l • • • . . • • • IS
4.5 Results of a Classical Rank Test Applied
to HIPLEX-l Test Cases • • • • • • • • • • 18
4.6 Representat.ive Draw Analysis. • . • • • • • • 20
4.7 Estimated MRPP P~Value Dependence on Suple
Size for HIPLEX-l • • • • • • • • • • • 20
5. PHYSICAL INVESTIGATIONS • • • • • • • • • • • • • • 24
5.1 Raindrop Site Distribut.ions and Z-R
Relationships in HIPLEX-l • • • • • • • • • • • 24
5.1.1 Characteristics of the data. • • • • • • • 24
5.1.2 Drop size distributions. • • • • • • • • • 25
5.1.3 Z-R relationships. • • • • • 27
5.1.4 Comparisons between aircraft
and radar data • • • • • • • • • • • • • 30
iv
TABLE OF ~Ta"S (continued)
5.2 Studies of Non·Test-Case Clouds ••••••••• 31
5.3 Mesoscale Analysis. • • • • • • • . • • • • • • • 3A.
5.4 Est~ates of Requirements for I-leasuring Rainfall
fTOIl Convecdve Complexes with Rain Gages. 35
5.4.1 SUlJUry of results •••••••••• 36
5.4.2 Principal conclusions. • • • • • • ~8
5.5 Comparison of Gage and Radar Measurements
of Rainfall from Convective COlllplexes • 39
5.5.1 Data acquisition and reduction • 40
5.5.2 Summary of results •••••••••••• 41
6. NUMERICAL CWUO MODELING STUDIES •• • • • • • • • • • 45
6.1 Addition of a Snow Field to the Model •••••• 46
6.2 Addition of Convergence Effects to the Model. • • 46
6.3 TiDle-Step Effects in the Model Rcsul ts • • • • • • 47
6.4 Simulation of Silver Iodide Seeding in the Model. 48
6.5 Dyn8Jl!ic and ~licrophysica1 Effects
of Silver Iodide Seeding . • • • • • • • • • • 48
6.6 Simulation of Dry Ice Seeding in the Model. 51
6.7 Sim.dation of IIIPLEX-l Test cases • • • • • 52
6.8 Co..parison of Model Outputs with Actual
HIPLEX-l Observations • • • • . • • • • • 54
6.9 SillUlation of Convective Precipitation
with the 1oIode1 60
7. SlMlARY M1) CQ;"CWSION • • 62
ACKM:».'L.EJ)(}(ENTS ••••••••
REFERENCES • • • • • • • • • • •
APPENDIX A: Coordination Meetings During Period
1 April 1981-30 Novelllber 1982 •••
APPENDIX B: mpl.EX-l: Experimental Design and
Response Variables ••.•••••
APPENDIX C: HIPLEX-I: Statistical Evaluation ••
APPENDIX D: List of Publications Prepared Under
This Contract ••••••••
APPENDIX E: List of Project Personnel •.•••.
63
70
71
103
l20
126
LIST OF FIGURES
Humber Title f!&!.
Four cUllI.llative drop she distributions from
HIPLEX-I Case No.9 (22 July 1979). with
overlapping sample volurucs 2.
Z-R scatter diagram for the composite drop
size data from all the HIPLEX-l test cases
froa 1979 and 1980 • 2.
Histograas showing the percent of seeded and
non-seeded 1978 clouds having various values
of average u.'C at 0, S, 8, and 10 lIin after
"treatment" tiJne • 32
Plot of average and standard deviation of
Johnson-Williams LWC for 1978 seeded and
non-seeded Class A clouds vs. tiJlle. 33
Median of the absolute values of the relative
errors in gage estimates of rainfall volwnes
as a function of the nlunber of gages
receiving rain from a complex 37
Scatter diagra. cOll1paring radar estimates
of rainfall volurues for convective
complexes with rainSlo'ath areas . 3.
COlllparison of frequency distributions of
IS-Illin rainfall events £rolll 21 June 1977
as observed by two different methods 41
Normal probability plot of the log ratios,
log(GER/RER), froll 21 June 1977 data • 42
Example of tillle plot of IS-Din rain amounts
for one gage location (GER' and RfR events) • 44
10 The accumulated rainfall vs. tillle since
model initialization in the seed and
non-seed versions 52
11 NlJIlericRI siJwlation at 72 lIin .cdel time of
HIPLEX-l Test Case No. 10, 23 July 1979
(Class A-I cloud) 54
vi
LISI' OF FIGURES (continued)
12 Profiles of state variables and wind cOlllpOnents
across cloud model domain at height 4.4 kID,
after 12 min of simulated time. • • • • • • • • Ss
13 Simulated aircraft sample of clouds taken 3.8 km
above ground at 57 min of model time, or about
S min after treatment tilQe • • • • • . • • • • • • 57
LIST OF TABLES
Estimated power (I-II) of HIPLEX~l MRPP tests
for high, low (actual), and conservative
seeding effects • • • • • • • • • • • • • • • 13
Point estimates and MRPP test results for the
final test statistics • • • • • . • • • • . 17
Univariate Tank test results ~ HIPLEX-l • • • • • 19
~eans and standard deviations of "representative
draw" variables • • • • • • • • • • • . . • • 21
Changes in MRPP univariate P-values for raw
data values if observed data sets weTe
doubled and tripled. • • • • • • • • • • • • • 22
Comparison of lIOdel generated and observed
cloud response variables - HIP23 • • • • • 43
COlllparisons for all cases producing clouds
in model ••• • • • • • . • • • • • • • • 58
Comparisons of precipitation estimates for
cases producing clouds in model • • • • • • 61
1. Itm!ODUCTION
This is the final technical report submitted by the South Dakota
School of Mines and Technology (School of Mines) on research carried
out under the subject contract. Under this contract. personnel of the
School's Institute of Atmospheric Sciences (lAS) assisted the Bureau of
Recllllllation (Bureau) of the U.S. Department of the Interior in the
design and evaluation of the HIPLEX pFlgralll. The work was carried out
in collaboration with personnel of Colorado State University (CSU).
who were responsible for carrying out DOst of the statistical work
required to fulfill the project objectives. Work under the contract
extended over a pe1'iod of five years. beginning in DecCMber of 1977.
A series of interim progress reports (Dennis et aI •• 1979. 1980;
Smith et al •• 1981) describe the basic adDinistrat'iVearrangements for
conductrnithe work. The CSU participation "'as carried out under a
subcontract negotiated with the School of ~lines. The interim reports
sumnarited progress on the research being carried out undeparate physical evaluations
of the measuresents are being conducted by various HIPLEX participants
to confirm the physical ur.derstanding of effects of seeding. As men­tioned
above, numerical simulations of the seeding experiments have
also been carried out to simulate the behavior of the tost case clouds
and their responses to the seeding treatrr.ents.
The research carried out under this contract can be divided into
four broad general categories:
The design and conduct of the HIPLEX-I experiaent,
including calculation of the response variables.
b. Statistical studies, including the statistical
evaluation of HIPLEX-l.
Physical analyses, related directly or indirectly to
HIPLEX-I or to contemplated follow-on experiments.
d. NUlI!erical cloud modeling studies, including sillulation
of the HIPLEX-I test cases.
In the following sections, brief SUJm'.aries of the research under each
of these four broad areas are presented.
3. TIlE DESIGN AND CONDUCT OF HIPLEX-l
A major portion of the effort under this contract was devoted to
assisting with the development of the experimental design for HIPLEX-l
and monitoring the conduct of the experiment. Work under the contract
included preparation of two of the appendices to the design document
(Interior, 1979):
Appendix B: Conceptual Models ano Physical Hypothesis,
by A. S. Dennis and Ii. D. Orville
b. Appendix E: Statistical Design and Evaluation, by
P. W. Mielke, Jr., ar.d A. S. Dennis
A manuscript discussing the design, conduct, and response variables of
the experiment is included as Appendix B to this report: it has been
submitted for consideration for journal publication. The manuscript
gives an overview of the experimental design and the conduct of the
experiment; provides a synopsis of the procedures used to calculate the
response variables; and tabulates their values for the 20 HIPLEX-l test
cases from 1979 and 1980.
Substantial contributions were made under this contract in the
following specific areas:
1. Establishment of the randomization procedure for allocating
treatments to experimental units.
2. The. formulation of the physical hypothesis.
3. Statement of the statistical hypotheses for the experiment.
4. Definitions of the response variables, including default
values, and the procedures used in collecting the data
and calculating values for the response variables.
S. Establishment of the multi-response peTlllUtation procedures
(~lRPP) used in conducting the statistical evaluation of
the experiment.
6. A partial simulation of the experiment, using data from
exploratory field studies carried out in 1977 and 1978,
to estimate the required sample size for the experiment.
7. Monitoring the conduct of the experiment in the field.
8. Calculating the radar-related response variables and
checking the calculations of the response variables made
by other IIIPLEX-l pllrticipants.
9. Issuing the "official" tabulation of the response variables.
The status of most of these aspects of HIPLEX-I is sullllllarited
adequately in Appendix B. Some additional colMlents on three of the
areas appear in the follo....ing subsections, and other sections of this
report deal with topics related to some of the other areas above.
3.1 The Randomiution Procedure
Section 4 of Appendix B outlines the double-blind type rando.hation
procedure et!lployed in HIPLEX-l. It nquired the preparation of one set
of "dispenser disable" randollli~ation envelopes, based on an unrestricted
randomization, to deteX'lline "tlich of the two dry ice dispensers on the
seeding aircraft was to be disabled for a given flight. One of those
envelopes was used before each flight, including flights on which no
suitable test case clouds were found.
Six additional sets of "dispenser selection" envelopes 101ere prepared
for use in detel'llining which dispenser should be activated by the crew
of the seeding aircraft once a candidate cloud had passed the selection
criteria for a particular class. Two sets of these envelopes ,,-ere needed
for each cloud class (A-I, A-2, or B), with the one used for a particular
flight being chosen according to which "dispenser disable" decision had
occurred. In that way, the restricted non_seed/seed randomization for
test cases wi thin each cloud class was preserved regardless of the disable
de 1494 s (24.9 _in), a radius of
20 km was used.
3. Determine which echoes were due to aircraft "skin paint"
reflections. This was done by a) coWlparing the time and
loeation of the echo with the positions of the aircraft
at that ti~\e; b) comparing .the echo height with the alti­tudes
of the aircraft at that time; and c) judging ....nether
the echo was continuous in time or only occurred on one
scan. The possibility of an echo being due to skin paint
was not considered if echoes ",ere recorrled in several
radllJ" data bins grouped together in an area, or if the
echo was recorded at several elevation angles.
lRPP large sample program
has been documented by Bert')' and Mielke (1983).
All of the above-cited papers (except the two preliminary papers)
were project papers which proVided substantial contributions to the
development of "IRPP. As a consequence of the effort summariz.ed above,
requests have been received from the editors of both the Handbook of
Statistics, Vol. 4, and the Encyclopedia 2! Statistics, ~o­prOVIde
sUl':IflIsry papers of MRPP.
A few additional papers not directly related to MRPP ",~re also
prepared during this contract. These illcluded a paper pertaining to a
theoretical distribution problem inherent in certain classical linear
rank test statistics (Mielke and Sen, 1981) and a paper on the Climax I
and II experiments (Mielke at ~ 198Ic). Furthel'll\ore, a chapter was
prepared for a book on statIStlcs in atmospheric science (?>lielke, 1982).
4.2 Preliminary Sample Size Estimates for HIPLEX-l
This section describes the procedure used for estimating the
sample sizes needed to detect specified seeding-induced changes in
IlIPLEX-l. This procedure was employed prior to the beginning of
HIPLEX-I and the resul ts were used to estimate the required length
of the experiment (see AppendiX E of Interior, 1979). Given specj­fied
values of the type I and type II error probabilities (a and S),
the sample size estimates were based on the Euclidean distance
version of the mul ti-response permutation procedures (MRPP).
In comparison to 1\-ell known power calculations for parametric
tests which assume an underlying normal distribution (or perhaps some
other well defined distribution), analogous calculations for pemutation
tests are exceedingly more difficult. In addition to the dependence
on (1) the level of significance; (2) the sample-size structure; and
(3) the fonn of the alternative hypothesiZe0.99 0.66 0.10
PIC8 >0.99 0.82 0.20
TIPI >0.99 >0.99 0.70
JOINT >0.99 >0.99 0.40
100 CICS »0.99 0.95 0.10
PIC8 »0.99 >0.97 0.60
TFPI »0.99 »0.99 >0.95
JOINT »0.99 »0.99 0.60
ISO CtCS »0.99 »0.95 0.20
PICa »0.99 »0.97 >0.95
TFPt »0.99 »0.99 »0.95
JOINT »0.99 »0.99 >0.95
200 CICS »0.99 »0.95 0.20
PICS »0.99 »0.97 »0.95
TIPI »0.99 »0.99 »0.95
JOINT »0.99 »0.99 »0.95
is most apt to resul t in larger precipitation part.icles It'hich would
survive evaporation losses below cloud base, and therefore result in
larger total rainfall on the ground. The high seeding rate, on the
other hnnd, i!' likely to achieve similar rl1in rates but with smaller
preclpitnting parUctes thnt are mort" vulnerable to evapor;'ltion tosses,
eVE!n though it: prorlu('('s effects in sollie of the l'esponse vtlritltes that
Catl be statlstic,ally recogni;:od with SJn811er somples. 11'1(0 hypothesi;:ed
conservative seeding effect was used to establish an upper lindt on
sa.ple she, should the actual seeding effects be IIUch maIler than
anticipated; it 1l'as also used as a test of the evaluation technique.
14
Based on the results of these simulations for the low (actual)
seeding rate effects, it appeared that SO to 100 samples (25 to 50
seeded, and 2S to SO non-seeded) would be required to reject the null
hypotheses in HIPLEX-l. It was, of course, assumed that the results
for the three response variates used in these sample.size calculations
were indicative of the results that could be expected for all of the
response variates and final test statistics.
4.3 Statistical Evaluation of HIPLEX-l
A statistical evaluation of the HIPLEX-l experiment was carried
out under this contract according to the evaluation plan outlined in
Chapters VI and X and Appendix E of the design document (Interior,
1979). A draft manuscript discussing the Tesul ts of that evaluation
appears as Appendix C to this report; it is being revised for submission
for journal publication.
The evaluation presented in Appendix C is based on the multi­response
permutation procedures (HRPP) discussed in Section 4.1. The
main results of the statistical evaluation of HIPLEX-l are as follows:
1. Pronounced differences were found between the response
variables measured in non-seeded and seeded clouds during
the first 5 min after treatment. Those variables are
associate PCPA
(b) PCPR
2. (a) A'iRA
(b) AVRC
(c) AVRR
Proportion of experimental units that precipitate,
based on the Time to initial E,recipitation at the
+lOC level, .!lrcraft measurement (TIPA).
Proportion of experimental units that precipitate,
~~~d1:ereS~;5t~a~;t~~~ ~:)i~~~;~~~n at the
Average volWl:e of precipitation per experiltenta1
unit, based on Aircraft estimated rainfall at the
+lOC level (AERT. - -
Average volume of precipitation per experimental
unit, based on Radar estilrlated rainfall at the +10C
level, using a ~onstailt Z-R relationship (RERC).
Average volume of precipitation per experimental
unit, based on Radar estimated rainfall at the +lOC
level, Z-R rcla"tionshlp adjusteo by hydroaeteor
measurements (RERA.). -
16
Table 2 presents the final test statistiC$. with point estilaates
and MRPP test resul t5. (AVRR was not calculated because values were
not obtainea for REM.; the reasons for that are discussed in Sec. 5.1.)
The P-values in that table are not based on the NRPP test statistic dis­cussed
in Appendix C. Instead, all the pern.utations of the HIPLEX-l
test cases in each class between non-seeded and seeded treatllents were
eTlUl:lerated and the various ratios indicated in the table were calculated
for each pcn:;utation. The P-values presented then indicate the £Taction
of those pemutations for which the ratio was as favorable (or IIlOrc
so) to the enhancement of precipitation by seeding as the neat:l:lent
allocation realized in the experiment. Unl!er the null hypothesis of
no seeding effect. the expected P-value l«luld therefore be 0.5. and
a Slllall value can be taken as evidence of a seeding effect.
Many of the values of the response variables that entered into
the determination of the final test statistics were default values,
and consequently fe.... of the final test statistics exhibi t significant
results. All the seed/non~seed differences in Table 2 are in the sense
indicated by the HIPLEX-I physical and statistical hypotheses except
that for AVRA (Class A-I). The seed/non-seed ratio for that case is
0.088, but that value is dominated by a single non-seeded test case
(HIPLEX-l Case No.7) and has no statistical significance. The AVRA
(Class B) ratio of 26.!1 has an associated P-value of 0.07S, rot that
result should also be vielo-ed with caution because the ratio is again
dolllinated by a single (seeded) test case (Cue No.9).
SoRe interesting questions are raised by the different proportions
of the test cases that "ere deemed to have produced rain, depeming upon
"nether TIPA (associated with PCPA) or AER (associated with AVRA) is
used to detemine the presence of rain. One IIIOre Class A-I cloud and
three IIOre Class B clouds "'Cre identified as producing precipitation
when AIR was used as the in0 00..; ........ 0 ....... :"'..;
k :rI ......:: .... - .... .. ~ , .. ..: ~:::::::::;:: ..
!1'
."\ ~~2~2!:::!::::: ::e:: :e::::::::!:: I!::. !!
!!!!!!!i!!R!i ~~~!~!!! !!I!! II i~
ggiimmm~ ~~~nit~ mn '.,
AAA'AA' ... .. J! ~n~mmn~ e!!:eEEEEe ~eeee EE
m~~m Hm i; ;::=
~~~I~!lf~~~!i ['~~Ig~~! mgg gg ~~i,
iimm ~~sn ,. :>]] .. "
I
gog
mmmmW eeeeeeee eEeEe iE ~~I~I iimm ?~H$ ~::! " i~I::1
"':";"';";";';,:"'::"';;"'''' -............ "'~ .. .~ .;~ ... .; ..- ..
20
between the non-seeded and seeded responses. The Sw:lS of the ranks
presented in Table 3 also indicate the senses of the differences.
They show. for eX8Ilple. that AweS in the seeded clouds tended to be
greater than AJIl'C8 in the non-seeded ones. contrary to the HIPLEX-I
physical hypothesis. The senses of the other priJlary responses are
generally consistent rith the physical hypothesis. alt.hough many of
the differences either have little statistical significance or are
alliOst non-edstent.
4.6 Representative DTaw Analysis
Several variables assodated with the HIPLEx-l test cases but not
subject to influence by the seeding were exuined in a search for pos­sible
bias due to a ''bad draw" in the random allocation beb'een the
seed and non-seed treatments. The results, considering the Class A~l
and B clouds combined, are sUltD'larited in Table 4. Some comments
follow:
Time Variables: Time of day and Julian dates of the
test cases were compared bet",een seed and non-seed
cases. Very little difference was found.
b. Seeding Temperatures: The temperatures at which
seeding "'as accoViplished were very close (-10.8C,
seed vs. -10.6C. non-seed). The temperatures were
mensured by the Learjet seeding aircraft.
Sounding Variables: Variables from the 2000 GIT
Milos City sounding were co_pared. AVf'rage values
of surface tCllperature. dew point, low level mois­ture,
lifted index, precipitable water, and wind
shear were very sillilar. There are sOllle indica­tions
of differences in the standard deviations of
the variables, but in vi~ of the small sample
size, these differences probably have little real
significance.
It appears fTOl:!'l these values that confidence can be placed in the
luck of the randomization draw in this experiment. Thus, greater con.
fic.ence can be placed in the statistical results of the experiment.
However, it would be useful to examine the variables measured by the
cloud physics aircraft on the pre-treatment pass (see Table I of
Appendix C) in a similar manner to identify any possible differences
among the individual test case clouds within each class.
4.7 Estimatco:l ~lRPP P-Value [lcpeno:lence on Sample Size for IlIPLr:x-l
To investigate the effect on the P-values for the HH'I,EX-l response
variables if brger slUIlples had been availilble, the existing samples
(4 seeded and 3 non-seeded cnses for Class A~l clouds; 8 seeded and 5
21
ABLE 4: Means and Standard Deviations of "Representat.ive Draw" Variables
Seeded Non-Seeded
Variable ~ ~
!No. of Cases 12 8
~ay of Year Mean (Julian) 182.3 185.0
Std. Dev. (days) 2S 13
ime of Treatment Mean (hr-Qrr) 20.70 20.08
Std. Dev. (hI') 0.93 1.58
Temperature at Meon (OC) -lO.S -10.6
Seeding Altitude Std. Dev. C'C) 1,6 1,1
Radiosonde Variables (2000 GMT)
Surface Temperature Mean (OC) 25.7 26.6
Std. Dev. C'C) 5.' 3.7
Surface Dew Point Nean rOC) 8.2 9 ••
Std. Dev. C'C) 4.1 2.9
Low Level Moisture Mean (g/kg) 6.2 6.7
(SO bPa mean) Std. Dev. (g/kg) 1,' 1.3
Lifting Condensation Level Mean (hPa) 71. 7.7
(using surface T Ii, T
d
) Std. Dev. (hPa) 54 60
Lifted Index ~lean (Oe) -1.3 -1.1
Std. Dev. C'C) 2,2 2.2
Precipitable Water ~:eari (em) 2,01 2.02
Std. Dev. C=) 0,63 0.41
Surface - SOO hPa Windshear Mean (kts) -" _21
22
non-seeded cases for Class B clouds) were doubled and tripled in size
to simulate an extended HIPLEX-I experiMent. The observed values for
selected response variables (PICS, TFE. and AER) "'ere simply replicated
the appropriate nUlllber of times and the resul ts analyzed with the MRPP
univariate test. The results of this investigation (for the raw data
values) are given in Table S.
As anticipated. the P_values become much smaller wi til. the larger
sample sizes. In ItOst instances, strong significance would have been
achieved if the sample size were tripled. That lleans that an extended
experil!ent rith about 60 test cases, which would be at the low end of
the original sample size estimates (see Sec. 4.2), could be expected
to give statistically significant resul ts for llIany of the HIPLEX-l
response variables. The relatively slo,," decrease of the P-values for
TFE in Table 5 appears to be due to the presence of tied no-echo cases
(TFF. "' 2400 s) in both seeded and non-seeded s8Jllples. The aforemen­tioned
60 cases, moreover, would be distributed about 20 in Class A-I
and 40 in Class B, so that significant results are possible for each
cloud class with sample sizes even smaller then the original estimates.
ABLE 5: Changes in MRPP univariate P-values for raw data values if
bserved data sets "'ere doubled and tripled (fOT the specific priJ:1ary
response variables PICS, TFE. and AER)
CLOUD CLASS
~ -'- ~
~
Original 5antple 0.143 0.428 0.289
Doubled Sample 0.113 0.145 0.076
Tripled sample 0.044 0.053 0.021
l!!
Original S8lIlpie 0.486 0.76) 0.505
Doubled Sample 0.276 0.499 0.250
Tripled S8lllple 0.148 0.347 0.135
~
Original Sample 1.000 0.110 0.578
noubled $ample 0.098 0.028 0.286
Tripled S3Jlplc O.02R O.OOR 0.149
23
It should be noted that these results arc based on an extrapolation
of the existing resul ts which are, in turn, dependent on the randomi­zation
realized in the HIPLEX-l experiment, as well as the physical
effects of the seeding. These simulations lI'IUst therefore be viewed
with some caution. For example, the "opposite sense" response of
AWC8 in the existing 20 HIPLEX-l test cases would not be reversed by
replicating the same cases. The AER results for Class A-I clouds in
Table S. although yielding P-values less than 0.1 for doubled or larger
saI1ple shes, are also associated with a sense opposite to that sug­gested
by the physical hypothesis. That is caused by the doIJinance of
one non-seeded test case (~. 7) in the rainfall 8lIIOunts; t.hat case
becomes replicated in the simulated extensions and continues to dominate
the response. Consequently, this simulated extension of HIPLEX-l
merely provides sample size estimates that, because they are based on
data from the actual experiment, should be improvements over the
pre-experiment estiT.lates discussed in Sec. 4.2.
24
S. PHYSICAL INVESTIGATIONS
Various physical studies ..-ere carried out under this cont.ract.
They included both physical evaluations of HIPLEX-I test case results
and studies of clouds not included as part of the fomal HIPLEX-I
randomized seeding experiaent. Mesonet data available f:r'01It the Miles
City area for the 1980 HIPLEX-l period were analyzed extensively.
So.e design studies for a cont~lateles used herein
were prepared according to the "mr.ber of particlu" method (Arnesen.
1982).
The second issue relates to problems with regression analysis.
Three candidate approaches were considered: Ordinary linear regres­sion
on the log-log Z-R scatter plot; linear regression taking account
of the eorrelation between the uncertainties in Z and R values deter­mined
from a drop she distribution (Mueller and Sims. 1966; Cooper
et a1 •• 1981); and me-dian regression (Mielke et al., 1981b). wich
reduces the sensitivity to outlier-type pointS:- Ai'ain, the issue as
28
to which approach is preferable has not been resolved. The results
presented below were obtained using ordinary linear regression, but
t.he advantages of the other methods lIlight well yield significant
illlprovelllents.
The third issue seems to be clearly resolved in favor of using
permutation procedures like IomPP to assess differences in Z.R rela­tionships
among test cases. or between seed and non-seed groups. Any
other approach involves assumptions about the distributions of the
points on the Z-R scatter diagram, in relation to the line of best
fit, that are difficult to substantiate.
The entire HIPLEX-l raindrop data set comprised 372 raw samples,
considering Class A-I and Class B clouds together. The Z-R relation­ship
fit to the points for the raw data snpies was Z • 130 Rl.82..
with a coefficient of determination r2 • 0.64. The composi ting
~~c~~~a~~~~pt::S~~e~3~fR~~l:~i;is.t~.i~~ a~e~~a~:lting
diaa.r8ll for the CODposite drop size data is shOl>"Il. in Fig. 2. Slight
differences ",-ere obtained in each case by perfonring separate
regressions on the seeded and non~seeded groups.
reroarr;:l;"'~i;i~a;c~~t~~~S~i~Sl;~eRt1~ed:;~~;:rf:: :~eO;~~:ization
analysis of radar and rain gage data from North Dakota (Smith et a1.,
1975). A possible explanation for the high eJtponents in theserela­t.
ionships is the coJmllon presence of graupe1 or hail in the showers,
;~~~~h~;~ ~~i~ri~u:~::~~i~fl;o~~:ft~~eZ2~-~3~IT'~f: 3ga~:~d ~e::;':~e
the radar rainfall estiMate RERC in IIIPLEX-l, although for Z > 30 dB:
the difference is within a factor 2.
The difference between points for each individual test case and
the rest of the cases was then assessed by using the NRPP. Pen!Utations
"'"ere determined by allocating the 141 points on the scatt.er diagru
randollly to the case under considerat.ion or the rest of the group. In
brief, the results showed that each individual test case differed
significantly f1'Olll the rest. with P-values as SClall as 10- 5 in soce
instances. However, regression lines fit t.o points for the individual
cases led, as often as nat, to bizarre z..R relationships; the exponent
was 6 in one case and 52 in another. 1h"t leaves us in tho awkward
posit.ion of being able to dmonstrate statistically significant differences
among the points on the l-R scatter diagram for the individual test cases,
while being unable to obtain plausible Z·R relationships on a case-by-case
basis.
Similar comparison of the seeded versus non-seeded groups led to a
sOllooat different quandry. When the MRPP comparison was "one case"
versus "the rest," individual points on the scatter diagrllJD could be
allocated randomly to either "one" or "the rest" to deteTlline the
10
COMPOSITE SAMPLES
x-NO-SEED
--SEED
_.x·
",
2.
E E ,.
w;r
'" ...J
...J
~
Z"
"'I
'0
pel1il.ltations. When the e6 x 1O-~ 5- 1, and the
spatially averaged wind divergence value over the salte area, at a given
time. Plots of the values on a cell basis and of the variance and
standard deviation of the values for the total network area at 15 min
intervals were produced. Radar Estimated Rain Volume (RERV) was calcu­lated
for each cell using an optTmhed Z-R-relationship (Smith et. aI ••
1975). The tiDe evolution of the areal divergence, the varianceoT"the
net divergence field over the whole net\o'Ork, the lllaXi~ radar reflec·
tivity factor, the total RERV aCCUlllUlations, and other quantities were
analyz;ed for each of the ten rain periods.
The structure of the mesoscale wind fields and their evolution
were found to be some"'ilat different in the dry »:mtana cliMate than
those found in humid climates. Collpared to the humid cliMates, the
areal divergence values in Io!ontana are 8-10 tillles larger. On the
other hand, the rain efficiency (total rainfall divided by total
1IlOisture inflow, and expressed in percent) was found to be less than
for stoms in b.naid cliJ:Iates. The stOl'll efficiency ranged between 2\
and 30\, with an average of 20\. and was lar£er for the larger storms.
A new q\lantity called the Areal Convergence Time Integral (ACTI)
was defined and found to be ",-eIT correlated with The RERV in a semilog
plot (r '" 0.92). The REPV was also found to be "'-ell correlated with
the tiJlle interval between the start of the intensification of the areal
convergence (>6 x 10-4 $-1) prior to the onset of rain and the start
of the rain (r '" 0.96). These facts suggest that the areal divergence
and the ACTI have potential as predictors for the start time of the
rain and t.he total rainfall aroount, respectively.
The variance of the wind divergence field for the whole network
area on each of the five days considered indicated a cyclic evolution.
The duration of the intensification period in the variance of the wind
divergence field, for the cycle occurring just prior to the beginning
of the period of rain, "'"as found to be correlated with the duration of
the rainfall (r'" 0.78). It is important to note, however, that this
was an exploratory study and the results are based on a very lilO'lited
sample she. Additional investigations with further data will be
necessary.
5.4 2O~:~~~~e02a:Pl~;~~:~h~~n~~::~~ini Rainfall fr&tes for ones that do
not tend to be large.
(b) A convective complex experiment that will include complexes
with rainswaths smaller than about 300 km2 cannot rely on gages alone
for measuring the rain volumes.
(e) Classification of the errors in rain measurements by the
number of gages receiving rain shows that five gage reports may be
sufficient to give median errors of less than 25\.
39
0'0 ......
" ..........
"
100-
0
1
10
1 I
100 103
RAIN$WATH AREA lkm2)
1
10'
~: Scatter diagI1la COllparina radar estimates of rainfall volumes
f'Ci'rCOnvective complexes 'ldth rainswath areas.
5.S Comparison of Gage and Radar MeaSUTelIIents of Rainfall foom
Convectlve Complexes
Because of the problems associated with attempting to measure
rainfall from convective complexes using gages indicated in the pre­ceding
section, any experilllent on convective complexes would probably
have to eMploy radar methods to lleasure the rainfall 8JIIOunts. It is
generally accepted that any prograa for radar .easur_ent of rainfall
should include comparisons between radar and gage estlutes of the
40
rain amounts. However. attempts to devise an operationally satis­factory
method of comparison are often frustrated by the variability
found when the radar and gage estimates of rainfall are compared.
This variability is illustrated and discussed in the present section,
which SUJl1m3rites the results of an examination of some radar and rain
gage data from the 1977 HIPLEX program in Montana (Meli ta, 1982).
Possible causes of the variability include the timing and positioning
errors involved in comparing data from separate sources, variability
in the gage measurements due to effects such as wind or evaporation,
variability in the R~Z relationships, and radar calibration
difficul ties.
5.5.1 Data acquisition and reduction
The radar data for this study were collected with the SIl'R-7S
digital weather radar data system located at Miles City. (It also
proVided the radar rainswath data discussed in Sec. S.4.) It is a
S.4-cm wavelength radar set with antenna beamwidth of 1". The radar
data used consisted of survey scans covering 360" in azimuth, made
at 1" elevation at S-min intervals. The raw radar data. essentially
integrated video signal levels recorded on tape, were converted. to
equivalent radar reflectivity factors. The radar reflectivity factor
was then abstracted for each gage location at each survey scan time.
Those values ....ere converted to rainfall rates using the Marshall­Palmer
relationship Z .. 200 Rl.6 and then integrated over time to
yield the "point" rainfall amounts.
A 109-si te rain gage network was operated in the project area,
with a network density of one gage per 15.5 kJt2 (6 sq mil. Each
site had at least one Belfort recording gage with daily chart rotation
that provided IS-min time resolution and 0.25 rom (0.01 in) quantity
resolution. The basic data are therefore IS-min rainfall totals for
each rain gage location, as measured by the gage and independently by
the radar systEmt.
For this study, the lS-miJl summations of radar estimated rainfall
(R£R) \,,.ere compared with gage estimated rainfall (GER) data at the same
time resolution for four days of interest. One measure of agreement
between GER and RER estimates of rainfall amounts is based upon the
logaritlun of their ratiO, 10g(GER/RER). Among the important charac­teristics
of this "log ratio" is its feature of preserving the sense
of any difference between radar and gage data: positive values corre~
spond to GER greater than RER and negative values to GER smaller than
RER. Ideally, all the log ratios should be zero, indicating perfect
ngreement between GER and RER. It has previously been noted that the
distdbutions of the log ratios tend to be approximately normal, which
cnn be 11 useful property (Cain and Smitll, 1977).
41
5.S.:? Summary of results
Figure 7 compares the frequency distributions of IS-JDin rainfall
allOunts as indicated by the radar and the gages for one particular
day. which is representative of the comparisons. The radar estilllltes
31'e seen to be generally lower than the gage estimates by about a
factor". In vicw of the exponent 1.6 in the l-R relationship used,
this would be equivalent to about a factor 10 discrepancy in the radar
reflectivity factors if the entire difference could be attributed to
radar errors. That is, if the errors were attributed entirely to the
radar data, a discrepancy of about 10 dB would be indicated in the
radar .easuremcnts at that tillie. Other indications suggested possible
radar ealibration errors of the same order of lllagnitude in the 1977
data, but a major evaluation of the radar "as carried oot in the fall
of 1977 (SIIith. 1977) and subsequent data are believed to be IllOre
accurate.
21 JUNE 1977
~
G:i 0.75
~o§
~Q50
§
5°·25 a
°10del Results
In the process of simulating the HIPLEX-I dry ice cloud seeding
experiments (see Sec. 6.6), an effect of changing the model time step
came to light (Orville and Hirsch, 1981). It appears that the model
results are sanewhat time-step dependent. even though a ti.Be step is
chosen that aaintains ro.erical stability. These results are
consistent with "'lin-Nielsen's work (1979) on larger scale IIOdels.
A time-step change is required in the model lihen dry ice is
introduced into a moderate-sized model cloud. The dry ice pellets
fall at speeds of 20 m s-1 or greater, while the model wind speeds
may be less than 10 m s-1. The time step required depends on the
largest velocity in the domain. Consequently, an automatic reduction
(often a halving) of the time step will often occur at the tac the
dry ice is introduced in the lIIOdel dOllain. Thfl clouds in TUns with
12 14 16 18 20
DISTANCE FROM LEFT BOUNDARY (km)
~: Profiles of state variables and wind components across cloud
~in at height 4.4 b:!. after 72 lIIin of silmlated tillle. Hori­zontal
and vertical ldnds (U and W). temperature, and pressure are
shown.
th~ physical hypothesis. Nevertheless. values for the various response
variables can be calculated from these cross sections and they do show
differences between the seeded and non-seeded versions (but not the
lIlaximull differences).
Figure 134 shows an example of the simulated cloud physics data from
the aode! output for the 22 June 1979 sounding. The snow mass concentration
(g .-3) and the ItUIllber concentrations of particles larger than 200 lim
diameter (~.t-l) and larger than 600 \.1m diameter (lte l ) are plotted
across the morlel domain at 57 min of model tilJ:e and at 3.8 btl above
ground level. At 4.8 kIn altitude. the values would be about 100 times
grellter. those samples corresponding more closely to the middle of
the cell. Th" growth of the model cloud pushed the IIItlld~\um concen­trations
of snow and cloud icc above the -8C level specified for the
cloud physics aircraft penetration in this instance.
The clouc: liquid water concentration (LWC), cloud ice mass
concentration and vertical velocity values are shown in Fig. 13b. The
LWC value of >2.0 g m- 3 is higher than the observed values for the test
case clouds on that day. The CIC5 value is obtained by taking the ice
mass concentration (IKC) from the lower curve and converting it to a
number concentration by assUDling an average size for the ice crystals
(10 )lm).
The stnte variables shown in Fig. 13(' give the temperature
variation through the cloud, as """ell as the velocity and pressure
variations. Other curves are available in the model printout for the
hail and rain mass concentration fields.
Table 7 shows a few of the HIPLEX-I response variables obtained
from model and aircraft observations for this case. Generally the
model cloud microphysical results arc lower than the observations
taken at the aircraft sampling altitudes. (But, as noted above,
higher values were present at higher altitudes in the 1I'.0del clouds.)
The times to first radar echo and first precipitating ice are shorter
in the model results than those observed in the field. The non-seeded
cloud actually studied never did reach a precipitation stage. but the
corresponding model cloud deVeloped precipitation at about 14 min
after treatment.
Thi s technique for simulating dry ice seeding of cumulus clouds
produced reasonable results for this test case. Model clouds formed
wi th relatively cool bases at about 2 Ian above ground level and developed
to a maximum height of about 6 Jon in the first surge. and to near 8 btl
in a second growth surge. The model clouds were not completely isolated,
so that the rain production depended on the interaction of one cell
with another. The seeded version exhibited stronger interaction of
one cell with another, because of the earlier formation of precipitation
in the seeded cloud. The resulting precipitation from the two cells
was about 20% more in the seeded version.
The model clouds were wetter and developed precipitation faster
than the actual clouds, possibly due to several items inherent in the
simulation. The actual clouds were generally shorter-lived and had
lower liquid I"ater concentrations. The specified initial conditions.
the eddy mixing coefficients. two-dimensionality of the model. or other
factors (known and unknown) may contribute to the differences between
the model and the actual clouds. Model resul ts for some days agree
57
!~r--- r
Fi'S/3: Simulated aircraft sample of clouds taken 3.8 bII above ground
at min of model tille. or about 5 -.in after treatment ti.e. (a) Snow
variables; (b) cloud variables: and (e) state variables. See text for
addi tional explanation.
58
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